Rs Aggarwal 2017 Solutions for Class 8 Math Chapter 20 Volume And Surface Area Of Solids are provided here with simple step-by-step explanations. These solutions for Volume And Surface Area Of Solids are extremely popular among Class 8 students for Math Volume And Surface Area Of Solids Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2017 Book of Class 8 Math Chapter 20 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2017 Solutions. All Rs Aggarwal 2017 Solutions for class Class 8 Math are prepared by experts and are 100% accurate.

Page No 222:

Question 1:

Find the volume, lateral surface area and the total surface area of the cuboid whose dimensions are:
(i) length = 22 cm, breadth = 12 cm and height = 7.5 cm
(ii) length = 15 m, breadth = 6 m and height = 9 dm
(iii) length = 24 m, breadth = 25 cm and height = 6 m
(iv) length = 48 cm, breadth = 6 dm and height = 1 m

Answer:

Volume of a cuboid =(Length×Breadth×Height) cubic units
Total surface area =2(lb+bh+lh) sq units
Lateral surface area =2l+b×h sq units

(i) Length = 22 cm, breadth = 12 cm, height = 7.5 cm
Volume =(Length×Breadth×Height) = (22×12×7.5)=1980 cm3
Total surface area =2(lb+bh+lh)= 222×12+22×7.5+12×7.5=2264+165+90=1038 cm2
Lateral surface area =2l+b×h=222+12×7.5=510 cm2

(ii) Length = 15 m, breadth = 6 m, height = 9 dm = 0.9 m
Volume =(Length×Breadth×Height) = (15×6×0.9)=81 m3
Total surface area=2(lb+bh+lh) = 215×6+15×0.9+6×0.9=290+13.5+5.4=217.8 m2
Lateral surface area =2l+b×h=215+6×0.9=37.8 m2

(iii) Length = 24 m, breadth = 25 cm = 0.25 m, height = 6 m
Volume =(Length×Breadth×Height) = (24×0.25×6)=36 m3
Total surface area=2(lb+bh+lh) = 224×0.25+24×6+0.25×6=26+144+1.5=303 m2
Lateral surface area =2l+b×h=224+0.25×6=291 m2

(iv) Length = 48 cm = 0.48 m, breadth = 6 dm = 0.6 m, height = 1 m
Volume =(Length×Breadth×Height) = (0.48×0.6×1)=0.288 m3
Total surface area =2(lb+bh+lh)= 20.48×0.6+0.48×1+0.6×1=20.288+0.48+0.6=2.736 m2
Lateral surface area =2l+b×h=20.48+0.6×1=2.16 m2

Page No 222:

Question 2:

The dimensions of a rectangular water tank are 2 m 75 cm by 1 m 80 cm by 1 m 40 cm. How many litres of water does it hold when filled to the brim?

Answer:

 1 m = 100 cm
Therefore, dimensions of the tank are:
2 m 75 cm× 1 m 80 cm× 1 m 40 cm=275 cm × 180 cm × 140 cm
∴ Volume =  Length × Breadth× Height = 275×180×140=6930000 cm3

Also, 1000cm3=1L

∴ Volume =69300001000=6930 L

Page No 222:

Question 3:

A solid rectangular piece of iron measures 1.05 m × 70 cm × 1.5 cm. Find the weight of this piece in kilograms if 1 cm3 of iron weighs 8 grams.

Answer:

1m=100cm
∴ Dimensions of the iron piece = 105 cm×70 cm×1.5 cm
Total volume of the piece of iron =(105×70×1.5)=11025 cm3
1 cm3 measures 8 gms.
∴Weight of the piece =11025 × 8 = 88200 g =882001000 = 88.2 kg                      because 1 kg = 1000 g

Page No 222:

Question 4:

The area of a courtyard is 3750 m2. Find the cost of covering it with gravel to a height of 1 cm if the gravel costs Rs 6.40 per cubic metre.

Answer:

1 cm = 0.01 m
Volume of the gravel used = Area × Height = (3750 × 0.01)=37.5 m3
Cost of the gravel is Rs 6.40 per cubic meter.
∴ Total cost =(37.5×6.4)= Rs 240

Page No 222:

Question 5:

How many persons can be accommodated in a hall of length 16 m. breadth 12.5 m and height 4.5 m, assuming that 3.6 m3 of air is required for each person?

Answer:

Total volume of the hall=(16×12.5×4.5)=900 m3

It is given that 3.6 m3 of air is required for each person.
The total number of persons that can be accommodated in that hall =Total volumeVolume required by each person= 9003.6=250 people 

Page No 222:

Question 6:

A cardboard box is 1.2 m long, 72 cm wide and 54 cm high. How many bars of soap can be put into it if each bar measures 6 cm × 4.5 cm × 4 cm?

Answer:

Volume of the cardboard box =(120×72×54)=466560 cm3

Volume of each bar of soap=(6×4.5×4)=108 cm3

Total number of bars of soap that can be accommodated in that box=Volume of the boxVolume of each soap=466560108=4320 bars

Page No 222:

Question 7:

The size of a matchbox is 4 cm × 2.5 cm × 1.5 cm. What is the volume of a packet containing 144 matchboxes? How many such packets can be placed in a carton of size 1.5 m × 84 cm × 60 cm?

Answer:

Volume occupied by a single matchbox=(4×2.5×1.5)=15 cm3

Volume of a packet containing 144 matchboxes =(15×144)=2160 cm3

Volume of the carton=(150×84×60)=756000 cm3

Total number of packets is a carton=Volume of the cartonVolume of a packet = 756002160=350 packets

Page No 222:

Question 8:

How many planks of size 2 m × 25 cm × 8 cm can be prepared from a wooden block 5 m long, 70 cm broad and 32 cm thick, assuming that there is no wastage?

Answer:

Total volume of the block =(500×70×32)=1120000 cm3
 
Total volume of each plank =200×25×8=40000 cm3=200×25×8=40000 cm3

∴ Total number of planks that can be made=Total volume of the blockVolume of each plank = 112000040000=28 planks

Page No 222:

Question 9:

How many bricks, each of size 25 cm × 13.5 cm × 6 cm, will be required to build a wall 8 m long, 5.4 m high and 33 cm thick?

Answer:

Volume of the brick =25×13.5×6=2025 cm3
Volume of the wall =800×540×33=14256000 cm3

Total number of bricks =Volume of the wallVolume of each brick=142560002025=7040 bricks  

Page No 222:

Question 10:

A wall 15 m long, 30 cm wide and 4 m high is made of bricks, each measuring 22 cm × 12.5 cm × 7.5 cm. If 112 of the total volume of the wall consists of mortar, how many bricks are there in the wall?

Answer:

Volume of the wall=1500×30×400=18000000 cm3
Total quantity of mortar=112×18000000=1500000 cm3
∴ Volume of the bricks=18000000-1500000=16500000 cm3

Volume of a single brick=22×12.5×7.5=2062.5 cm3

∴ Total number of bricks=Total volume of the bricksVolume of a single brick=165000002062.5=8000 bricks

Page No 222:

Question 11:

Find the capacity of a rectangular cistern in litres whose dimensions are 11.2 m × 6 m × 5.8 m. Find the area of the iron sheet required to make the cistern.

Answer:

Volume of the cistern=11.2×6×5.8=389.76 m3=389.76×1000=389760 litres

Area of the iron sheet required to make this cistern = Total surface area of the cistern
=2(11.2×6+11.2×5.8+6×5.8)=2(67.2+64.96+34.8)=333.92 cm2

Page No 222:

Question 12:

The volume of a block of gold is 0.5 m3. If it is hammered into a sheet to cover an area of 1 hectare, find the thickness of the sheet.

Answer:

Volume of the block=0.5 m3
We know:
 1 hectare = 10000 m2
Thickness=VolumeArea=0.510000= 0.00005 m= 0.005 cm = 0.05 mm

Page No 222:

Question 13:

The rainfall recorded on a certain day was 5 cm. Find the volume of water that fell on a 2-hectare field.

Answer:

Rainfall recorded = 5 cm = 0.05 m
Area of the field = 2 hectare =  2×10000 m2  = 20000 m2
Total rain over the field = Area of the field × Height of the field = 0.05× 20000 = 1000 m3

Page No 222:

Question 14:

A river 2 m deep and 45 m wide is flowing at the rate of 3 km/h. Find the quantity of water that runs into the sea per minute.

Answer:

Area of the cross-section of river =45×2=90 m2

Rate of flow=3 kmhr=3×100060=50 mmin

Volume of water flowing through the cross-section in one minute =90×50=4500 m3 per minute

Page No 222:

Question 15:

A pit 5 m long and 3.5 m wide is dug to a certain depth. If the volume of earth taken out of it is 14 m3, what is the depth of the pit?

Answer:

Let the depth of the pit be d m.
Volume = Length × width × depth = 5 m × 3.5 m× d m
But,
Given volume = 14 m3
∴ Depth = d =volumelength × width=145×3.5=0.8 m = 80 cm

Page No 222:

Question 16:

A rectangular water tank is 90 cm wide and 40 cm deep. If it can contain 576 litres of water, what is its length?

Answer:

Capacity of the water tank =576 litres=0.576 m3
Width = 90 cm = 0.9 m
Depth = 40 cm = 0.4 m

Length = =capacitywidth×depth=0.5760.9×0.4=1.600 m



Page No 223:

Question 17:

A beam of wood is 5 m long and 36 cm thick. It is made of 1.35 m3 of wood. What is the width of the beam?

Answer:

Volume of the beam=1.35 m3

Length = 5 m

Thickness = 36 cm = 0.36 m

Width = =volumethickness×length=1.355×0.36=0.75 m=75 cm

Page No 223:

Question 18:

The volume of a room is 378 m3 and the area of its floor is 84 m2. Find the height of the room.

Answer:

Volume = height × area
Given:
 Volume  = 378 m3
Area = 84 m2

∴ Height =volumearea=37884=4.5 m

Page No 223:

Question 19:

A swimming pool is 260 m long and 140 m wide. If 54600 cubic metres of water is pumped into it, find the height of the water level in it.

Answer:

Length of the pool = 260 m
Width of the pool = 140 m

Volume of water in the pool = 54600 cubic metres

∴ Height of water =volumelength×width=54600260×140=1.5 metres

Page No 223:

Question 20:

Find the volume of wood used to make a closed box of outer dimensions 60 cm × 45 cm × 32 cm, the thickness of wood being 2.5 cm all around.

Answer:

External length = 60 cm
External width = 45 cm
External height = 32 cm

External volume of the box=60×45×32=86400 cm3

Thickness of wood = 2.5 cm

∴  Internal length =60-(2.5×2)=55 cm
Internal width =45-(2.5×2)=40 cm
Internal height =32-(2.5×2)=27 cm

Internal volume of the box= 55 × 40 × 27 = 59400 cm3

Volume of wood = External volume - Internal volume= 86400 - 59400 = 27000 cm3

Page No 223:

Question 21:

Find the volume of iron required to make an open box whose external dimensions are 36 cm × 25 cm × 16.5 cm, the box being 1.5 cm thick throughout. If 1 cm3 of iron weighs 8.5 grams, find the weight of the empty box in kilograms.

Answer:

External length = 36 cm
External width = 25 cm
External height = 16.5 cm

External volume of the box= 36 × 25 × 16.5 = 14850 cm3

Thickness of iron = 1.5 cm

∴ Internal length =36-(1.5×2)=33 cm
Internal width =25-(1.5×2)=22 cm
Internal height =16.5- 1.5=15 cm  (as the box is open)

Internal volume of the box= 33 × 22 × 15 = 10890 cm3

Volume of iron = External volume − Internal volume= 14850 - 10890 = 3960 cm3

Given: 
1 cm3 of iron = 8.5 grams

Total weight of the box = 3960 × 8.5 = 33660 grams = 33.66 kilograms

Page No 223:

Question 22:

A box with a lid is made of wood which is 3 cm thick. Its external length, breadth and height are 56 cm, 39 cm and 30 cm respectively. Find the capacity of the box. Also find the volume of wood used to make the box.

Answer:

External length = 56 cm
External width = 39 cm
External height = 30 cm

External volume of the box=56 × 39 × 30 = 65520 cm3

Thickness of wood = 3 cm

∴ Internal length =56-(3×2)=50 cm
Internal width =39-(3×2)=33 cm
Internal height =30-(3×2)=24 cm

Capacity of the box = Internal volume of the box= 50 × 33 × 24 = 39600 cm3

Volume of wood = External volume − Internal volume= 65520 - 39600 = 25920 cm3

Page No 223:

Question 23:

The external dimensions of a closed wooden box are 62 cm, 30 cm and 18 cm. If the box is made of 2-cm-thick wood, find the capacity of the box.

Answer:

External length = 62 cm
External width = 30 cm
External height = 18 cm

∴ External volume of the box=62×30×18=33480 cm3

Thickness of the wood = 2 cm

Now, internal length =62-(2×2)=58 cm
Internal width =30-(2×2)=26 cm
Internal height =18-(2×2)=14 cm

∴ Capacity of the box = internal volume of the box=(58×26×14) cm3=21112 cm3

Page No 223:

Question 24:

A closed wooden box 80 cm long, 65 cm wide and 45 cm high, is made of 2.5-cm-thick wood. Find the capacity of the box and its weight if 100 cm3 of wood weighs 8 g.

Answer:

External length = 80 cm
External width = 65 cm
External height = 45 cm

∴ External volume of the box=80×65×45=234000 cm3

Thickness of the wood = 2.5 cm

Then internal length=80-(2.5×2)=75 cm
Internal width =65-(2.5×2)=60 cm
Internal height =45-(2.5×2)=40 cm

Capacity of the box = internal volume of the box=(75×60×40) cm3=180000 cm3

Volume of the wood = external volume − internal volume=(234000-180000) cm3=54000 cm3

It is given that 100 cm3 of wood  weighs 8 g.

∴ Weight of the wood =54000100×8 g=4320 g=4.32 kg

Page No 223:

Question 25:

Find the volume, lateral surface area and the total surface area of a cube each of whose edges measures:
(i) 7 m
(ii) 5.6 cm
(iii) 8 dm 5 cm

Answer:

(i) Length of the edge of the cube = a = 7 m
Now, we have the following:
​Volume=a3=73=343 m3
Lateral surface area =4a2=4×7×7=196 m2
Total Surface area=6a2=6×7×7=294 m2

(ii) Length of the edge of the cube = a = 5.6 cm
​Now, we have the following:
Volume=a3=5.63=175.616 cm3
Lateral surface area =4a2=4×5.6×5.6=125.44 cm2
Total Surface area=6a2=6×5.6×5.6=188.16 cm2

(iii) Length of the edge of the cube = a = 8 dm 5 cm = 85 cm
​Now, we have the following:
Volume=a3=853=614125 cm3
Lateral surface area =4a2=4×85×85=28900 cm2
Total Surface area=6a2=6×85×85=43350 cm2

Page No 223:

Question 26:

The surface area of a cube is 1176 cm2. Find its volume.

Answer:

Let a be the length of the edge of the cube.
Total surface area=6a2=1176 cm2
a=11766=196=14 cm
 ∴ Volume=a3=143=2744 cm3

Page No 223:

Question 27:

The volume of a cube is 729 cm3. Find its surface area.

Answer:

Let a be the length of the edge of the cube.

Then volume =a3=729 cm3

Also, a=7293=9 cm

∴ Surface area=6a2=6×9×9=486 cm2

Page No 223:

Question 28:

The dimensions of a metal block are 2.25 m by 1.5 m by 27 cm. It is melted and recast into cubes, each of side 45 cm. How many cubes are formed?

Answer:

1 m = 100 cm
Volume of the original block =225×150×27=911250 cm3

Length of the edge of one cube = 45 cm
Then volume of one cube=453=91125 cm3

∴ Total number of blocks that can be cast =volume of the blockvolume of one cube=91125091125=10

Page No 223:

Question 29:

If the length of each edge of a cube is doubled, how many times does its volume become? How many times does its surface area become?

Answer:

Let a be the length of the edge of a cube.
Volume of the cube=a3
Total surface area=6a2

If the length is doubled, then the new length becomes 2a.
Now, new volume =(2a)3=8a3
Also, new surface area==6(2a)2=6×4a2=24a2 
∴ The volume is increased by a factor of 8, while the surface area increases by a factor of 4.

Page No 223:

Question 30:

A solid cubical block of fine wood costs Rs 256 at Rs 500 per m2. Find its volume and the length of each side.

Answer:

Cost of wood = Rs 500/m3

Cost of the given block = Rs 256

∴ Volume of the given block =a3=256500=0.512 m3 = 512000 cm3

Also, length of its edge = a =0.5123=0.8 m = 80 cm



Page No 227:

Question 1:

Find the volume, curved surface area and total surface area of each of the cylinders whose dimensions are:
(i) radius of the base = 7 cm and height = 50 cm
(ii) radius of the base = 5.6 m and height = 1.25 m
(iii) radius of the base = 14 dm and height = 15 m

Answer:

Volume of a cylinder = πr2 h
Lateral surface=2πrh
Total surface area =2πr(h+r)

(i) Base radius = 7 cm; height = 50 cm
Now, we have the following:
Volume=227×7×7×50=7700 cm3
Lateral surface area=2πrh=2×227×7×50=2200 cm2
Total surface area =2πr(h+r)=2×227×750+7=2508 cm2

(ii) Base radius = 5.6 m; height = 1.25 m
Now, we have the following:
Volume=227×5.6×5.6×1.25=123.2 m3
Lateral surface area=2πrh=2×227×5.6×1.25=44 m2
Total surface area =2πr(h+r)=2×227×5.61.25+5.6=241.12 m2

(iii) Base radius = 14 dm = 1.4 m, height = 15 m
Now, we have the following:
Volume=227×1.4×1.4×15=92.4 m3
Lateral surface area=2πrh=2×227×1.4×15=132 m2
Total surface area =2πr(h+r)=2×227×1.415+1.4=144.32 cm2

Page No 227:

Question 2:

A milk tank is in the form of a cylinder whose radius is 1.5 m and height is 10.5 m. Find the quantity of milk in litres that can be stored in the tank.

Answer:

r = 1.5 mh = 10.5 mCapacity of the tank=volume of the tank = πr2h = 227×1.5×1.5×10.5=74.25 m3We know that 1 m3=1000 L 74.25 m3=74250 L

Page No 227:

Question 3:

A wooden cylindrical pole is 7 m high and its base radius is 10 cm. Find its weight if the wood weighs 225 kg per cubic metre.

Answer:

Height = 7 m
Radius = 10 cm = 0.1 m
Volume=πr2h=227×0.1×0.1×7=0.22 m3
Weight of wood = 225 kg/m3
∴ Weight of the pole=0.22×225=49.5 kg

Page No 227:

Question 4:

Find the height of the cylinder whose volume is 1.54 m3 and diameter of the base is 140 cm?

Answer:

Diameter = 2r = 140 cm
i.e., radius, r = 70 cm = 0.7 m

Now, volume â€‹=πr2h=1.54 m3

227×0.7×0.7×h=1.54 h=1.54×70.7×0.7×22=154×7154×7=1 m

Page No 227:

Question 5:

The volume of a circular iron rod of length 1 m is 3850 cm3. Find its diameter.

Answer:

Volume=πr2h=3850 cm3
Height = 1 m =100 cm

Now, radius, r=3850π×h=3850×722×100=1.75×7=3.5 cm
∴ Diameter =2(radius) =2×3.5=7 cm

Page No 227:

Question 6:

A closed cylindrical tank of diameter 14 m and height 5 m is made from a sheet of metal. How much sheet of metal will be required?

Answer:

Diameter = 14 m
Radius =142=7 m
Height = 5 m

∴ Area of the metal sheet required = total surface area

 =2πr(h+r)=2×227×7(5+7) m2=44×12 m2=528 m2

Page No 227:

Question 7:

The circumference of the base of a cylinder is 88 cm and its height is 60 cm. Find the volume of the cylinder and its curved surface area.

Answer:

Circumference of the base = 88 cm
Height = 60 cm

Area of the curved surface =circumference×height=88×60=5280 cm2
Circumference =2πr=88 cm
Then radius=r=882π=88×72×22=14 cm
∴ Volume=πr2h=227×14×14×60=36960 cm3

Page No 227:

Question 8:

The lateral surface area of a cylinder of length 14 m is 220 m2. Find the volume of the cylinder.

Answer:

Length = height = 14 m
Lateral surface area=2πrh=220 m2
Radius =r=2202πh=220×72×22×14=104=2.5 m
∴ Volume=πr2h=227×2.5×2.5×14=275 m3  

Page No 227:

Question 9:

The volume of a cylinder of height 8 cm is 1232 cm3. Find its curved surface area and the total surface area.

Answer:

Height = 8 cm
Volume=πr2h=1232 cm3
Now, radius=r=1232πh=1232×722×8=49=7cm
Also, curved surface area =2πrh=2×227×7×8=352 cm2
∴ Total surface area =2πr(h+r)=2×227×7×8+2×227×72=352+308=660 cm2

Page No 227:

Question 10:

The radius and height of a cylinder are in the ratio 7 : 2. If the volume of the cylinder is 8316 cm3, find the total surface area of the cylinder.

Answer:

We have: radiusheight=72
i.e., r=72h
Now, volume =πr2h=π72h2h=8316 cm3
227×72×72×h3=8316h3=8316×211×7=108×2=216h=2163=6 cm

Then r=72h=72×6=21 cm
∴ Total surface area =2πr(h+r)=2×227×21×(6+21)=3564 cm2

Page No 227:

Question 11:

The curved surface area of a cylinder is 4400 cm2 and the circumference of its base is 110 cm. Find the volume of the cylinder.

Answer:

Curved surface area =2πrh=4400 cm2
Circumference =2πr=110 cm
Now, height=h=curved surface areacircumference=4400110=40 cm

Also, radius, r=44002πh=4400×72×22×40=352

∴ Volume=πr2h=227×352×352×40=22×5×35×10=38500 cm3

Page No 227:

Question 12:

A particular brand of talcum powder is available in two packs, a plastic can with a square base of side 5 cm and of height 14 cm, or one with a circular base of radius 3.5 cm and of height 12 cm. Which of them has greater capacity and by how much?

Answer:

For the cubic pack:
Length of the side, a = 5 cm
Height = 14 cm
Volume=a2h=5×5×14=350 cm3

For the cylindrical pack:
Base radius =r=3.5 cm
Height = 12 cm
Volume=πr2h=227×3.5×3.5×12=462 cm3

We can see that the pack with a circular base has a greater capacity than the pack with a square base.
Also, difference in volume=462-350=112 cm3

Page No 227:

Question 13:

Find the cost of painting 15 cylindrical pillars of a building at Rs 2.50 per square metre if the diameter and height of each pillar are 48 cm and 7 metres respectively.

Answer:

Diameter = 48 cm
Radius = 24 cm = 0.24 m
Height = 7 m

Now, we have:
Lateral surface area of one pillar=πdh=227×0.48×7=10.56 m2
Surface area to be painted = total surface area of 15 pillars =10.56×15=158.4 m2
∴ Total cost=Rs (158.4×2.5)=Rs 396

Page No 227:

Question 14:

A rectangular vessel 22 cm by 16 cm by 14 cm is full of water. If the total water is poured into an empty cylindrical vessel of radius 8 cm, find the height of water in the cylindrical vessel.

Answer:

Volume of the rectangular vessel =22×16×14=4928 cm3
Radius of the cylindrical vessel = 8 cm
Volume=πr2h

As the water is poured from the rectangular vessel to the cylindrical vessel, we have:
Volume of the rectangular vessel  = volume of the cylindrical vessel

∴ Height of the water in the cylindrical vessel=volumeπr2=4928×722×8×8=28×78=492=24.5 cm

Page No 227:

Question 15:

A piece of ductile metal is in the form of a cylinder of diameter 1 cm and length 11 cm. It is drawn out into a wire of diameter 1 mm. What will be the length of the wire so obtained?

Answer:

Diameter of the given wire = 1 cm
Radius = 0.5 cm
Length = 11 cm
Now, volume=πr2h=227×0.5×0.5×11=8.643 cm3
The volumes of the two cylinders would be the same.
Now, diameter of the new wire = 1 mm = 0.1 cm
Radius = 0.05 cm
∴ New length =volumeπr2=8.643×722×0.05×0.05=1100.02 cm ≅ 11 m

Page No 227:

Question 16:

A solid cube of metal each of whose sides measures 2.2 cm is melted to form a cylindrical wire of radius 1 mm.  Find the length of the wire so obtained.

Answer:

Length of the edge, a = 2.2 cm
Volume of the cube =a3=2.23=10.648 cm3
Volume of the wire=πr2h
Radius = 1 mm = 0.1 cm
As volume of cube = volume of wire, we have:

h=volumeπr2=10.648×722×0.1×0.1=338.8 cm

Page No 227:

Question 17:

How many cubic metres of earth must be dug out to sink a well which is 20 m deep and has a diameter of 7 metres? If the earth so dug out is spread over a rectangular plot 28 m by 11 m, what is the height of the platform so formed?

Answer:

Diameter = 7 m
Radius = 3.5 m
​Depth = 20 m

​Volume of the earth dug out =πr2h=227×3.5×3.5×20=770 m3
Volume of the earth piled upon the given plot=28×11×h=770 m3

 h=77028×11=7028=2.5 m

Page No 227:

Question 18:

A well of inner diameter 14 m is dug to a depth of 12 m. Earth taken out of it has been evenly spread all around it to a width of 7 m to form an embankment. Find the height of the embankment so formed.

Answer:

Inner diameter = 14 m
i.e., radius = 7 m
Depth = 12 m
​Volume of the earth dug out=πr2h=227×7×7×12=1848 m3

Width of embankment = 7 m
Now, total radius =7+7=14 m

Volume of the embankment=total volume - inner volume=πro2h-πri2h=πhro2-ri2=227h142-72=227h196-49=227h×147=21×22h=462×h m3

Since volume of embankment = volume of earth dug out, we have:
1848=462 h
h=1848462=4 m
∴ Height of the embankment = 4 m

Page No 227:

Question 19:

A road roller takes 750 complete revolutions to move once over to level a road. Find the area of the road if the diameter of the road roller is 84 cm and its length is 1 m.

Answer:

Diameter = 84 cm
i.e., radius = 42 cm
Length = 1 m = 100 cm
Now, lateral surface area =2πrh=2×227×42×100=26400 cm2
∴ Area of the road =lateral surface area × no. of rotations=26400×750=19800000 cm2=1980 m2



Page No 228:

Question 20:

A cylinder is open at both ends and is made of 1.5-cm-thick metal. Its external diameter is 12 cm and height is 84 cm. What is the volume of metal used in making the cylinder? Also, find the weight of the cylinder if 1 cm3 of the metal weighs 7.5 g.

Answer:

Thickness of the cylinder = 1.5 cm
External diameter = 12 cm
i.e., radius = 6 cm
also, internal radius = 4.5 cm
Height = 84 cm

Now, we have the following:
Total volume=πr2h=227×6×6×84=9504 cm3
Inner volume =πr2h=227×4.5×4.5×84=5346 cm3
Now, volume of the metal = total volume − inner volume   =9504-5346=4158 cm3
∴ Weight of iron =4158×7.5= 31185 g= 31.185 kg   [Given: 1 cm3=7.5g]

Page No 228:

Question 21:

The length of a metallic tube is 1 metre, its thickness is 1 cm and its inner diameter is 12 cm. Find the weight of the tube if the density of the metal is 7.7 grams per cubic centimetre.

Answer:

Length = 1 m = 100 cm
Inner diameter = 12 cm
Radius = 6 cm
Now, inner volume=πr2h=227×6×6×100=11314.286 cm3
Thickness = 1 cm
Total radius = 7 cm

Now, we have the following:
Total volume=πr2h=227×7×7×100=15400 cm3
Volume of the tube =total volume-inner volume= 15400-11314.286=4085.714 cm3
Density of the tube = 7.7 g/cm3
∴ Weight of the tube =volume×density=4085.714×7.7=31459.9978 g=31.459 kg

Page No 228:

Question 1:

Tick (✓) the correct answer:
The maximum length of a pencil that can be kept in a rectangular box of dimensions 12 cm × 9 cm × 8 cm, is
(a) 13 cm
(b) 17 cm
(c) 18 cm
(d) 19 cm

Answer:

(b) 17
  
Length of the diagonal of a cuboid =l2+b2+h2

l2+b2+h2=122+92+82=144+81+64=289=17 cm

Page No 228:

Question 2:

Tick (✓) the correct answer:
The total surface area of a cube is 150 cm2. Its volume is
(a) 216 cm3
(b) 125 cm3
(c) 64 cm3
(d) 1000 cm3

Answer:

(b) 125 cm3

Total surface area =6a2=150 cm2, where a is the length of the edge of the cube.
6a2=150
a=1506=25=5 cm
∴ Volume=a3=53=125 cm3

Page No 228:

Question 3:

Tick (✓) the correct answer:
The volume of a cube is 343 cm3. Its total surface area is
(a) 196 cm2
(b) 49 cm2
(c) 294 cm2
(d) 147 cm2

Answer:

(c) 294 cm2

Volume=a3=343 cm3
a=3433=7 cm
∴ Total surface area=6a2=6×7×7=294 cm2

Page No 228:

Question 4:

Tick (✓) the correct answer:
The cost of painting the whole surface area of a cube at the rate of 10 paise per cm2 is Rs 264.60. Then, the volume of the cube is
(a) 6859 cm3
(b) 9261 cm3
(c) 8000 cm3
(d) 10648 cm3

Answer:

(b) 9261 cm3

Rate of painting = 10 paise per sq cm = Rs 0.1/cm2
Total cost = Rs 264.60
Now, total surface area  =264.60.1=2646 cm2
Also, length of edge, a =26466=441=21 cm
 Volume= 213=9261 cm3

Page No 228:

Question 5:

Tick (✓) the correct answer:
How many bricks, each measuring 25 cm × 11.25 cm × 6 cm, will be needed to build a wall 8 m long, 6 m high and 22.5 cm thick?
(a) 5600
(b) 6000
(c) 6400
(d) 7200

Answer:

(c) 6400

Volume of each brick=25×11.25×6=1687.5 cm3
Volume of the wall=800×600×22.5=10800000 cm3
∴  No. of bricks =108000001687.5=6400 

Page No 228:

Question 6:

Tick (✓) the correct answer:
How many cubes of 10 cm edge can be put in a cubical box of 1 m edge?
(a) 10
(b) 100
(c) 1000
(d) 10000

Answer:

(c) 1000

Volume of the smaller cube=(10 cm)3=1000 cm3
Volume of box=(100 cm)3=1000000 cm3     [1 m = 100 cm]
∴ Total no. of cubes =100×100×10010×10×10=1000

Page No 228:

Question 7:

Tick (✓) the correct answer:
The edges of a cuboid are in the ratio 1 : 2 : 3 and its surface area is 88 cm2. The volume of the cuboid is
(a) 48 cm3
(b) 64 cm3
(c) 96 cm3
(d) 120 cm3

Answer:

(a) 48 cm3

Let a be the length of the smallest edge.
Then the edges are in the proportion a : 2a : 3a.
Now, surface area=2(a×2a+a×3a+2a×3a)=2(2a2+3a2+6a2)=22a2=88 cm2
a=8822=4=2
Also, 2a = 4 and 3a = 6
∴ Volume=a×2a×3a=2×4×6=48 cm3

Page No 228:

Question 8:

Tick (✓) the correct answer:
Two cubes have their volumes in the ratio 1 : 27. The ratio of their surface areas is
(a) 1 : 3
(b) 1 : 9
(c) 1 : 27
(d) none of these

Answer:

(b) 1: 9

Volume 1Volume 2=127=a3b3a=b273=b3or b = 3aor ba=3
Now, surface area 1surface area 2=6a26b2=a2b2=(b/3)2b2= 19 Ratio of the surface areas = 1 : 9

Page No 228:

Question 9:

Tick (✓) the correct answer:
The surface area of a (10 cm × 4 cm × 3 cm) brick is
(a) 84 cm2
(b) 124 cm2
(c) 164 cm2
(d) 180 cm2

Answer:

(c) 164 sq cm  

Surface area =2(10×4+10×3+4×3)=2(40+30+12)=164 cm2

Page No 228:

Question 10:

Tick (✓) the correct answer:
An iron beam is 9 m long, 40 cm wide and 20 cm high. If 1 cubic metre of iron weighs 50 kg, what is the weight of the beam?
(a) 56 kg
(b) 48 kg
(c) 36 kg
(d) 27 kg

Answer:

(c) 36 kg

Volume of the iron beam =9×0.4×0.2=0.72 m3
∴ Weight=0.72×50=36 kg



Page No 229:

Question 11:

Tick (✓) the correct answer:
A rectangular water reservoir contains 42000 litres of water. If the length of reservoir is 6 m and its breadth is 3.5 m, the depth of the reservoir is
(a) 2 m
(b) 5 m
(c) 6 m
(d) 8 m

Answer:

(a) 2 m

42000 L = 42 m3
Volume=lbh
 Height (h)=volumelb=426×3.5=66×0.5=2 m

Page No 229:

Question 12:

Tick (✓) the correct answer:
The dimensions of a room are (10 m × 8 m × 3.3 m). How many men can be accommodated in this room if each man requires 3 m3 of space?
(a) 99
(b) 88
(c) 77
(d) 75

Answer:

(b) 88  

Volume of the room=10×8×3.3=264 m3
One person requires 3 m3. 
∴ Total no. of people that can be accommodated=2643=88

Page No 229:

Question 13:

Tick (✓) the correct answer:
A rectangular water tank is 3 m long, 2 m wide and 5 m high. How many litres of water can it hold?
(a) 30000
(b) 15000
(c) 25000
(d) 35000

Answer:

(a) 30000

Volume=3×2×5=30 m3=30000 L

Page No 229:

Question 14:

Tick (✓) the correct answer:
The area of the cardboard needed to make a box of size 25 cm × 15 cm × 8 cm will be
(a) 390  cm2
(b) 1390 cm2
(c) 2780 cm2
(d) 1000 cm2

Answer:

(b) 1390 cm2

Surface area=2(25×15+15×8+25×8)=2(375+120+200)=1390 cm2

Page No 229:

Question 15:

Tick (✓) the correct answer:
The diagonal of a cube measures 43 cm. Its volume is
(a) 8 cm3
(b) 16 cm3
(c) 27 cm3
(d) 64 cm3

Answer:

(d) 64 cm2

Diagonal of the cube=a3=43 cm
i.e., a = 4 cm
∴ Volume=a3=43=64 cm3

Page No 229:

Question 16:

Tick (✓) the correct answer:
The diagonal of a cube is 93 cm long. Its total surface area is
(a) 243 cm2
(b) 486 cm2
(c) 324 cm2
(d) 648 cm2

Answer:

(b) 486 sq cm

Diagonal =3a cm = 93cm
i.e., a = 9
∴ Total surface area =6a2=6×81=486 cm2

Page No 229:

Question 17:

Tick (✓) the correct answer:
If each side of a cube is doubled then its volume
(a) is doubled
(b) becomes 4 times
(c) becomes 6 times
(d) becomes 8 times

Answer:

(d) If each side of the cube is doubled, its volume becomes 8 times the original volume.

Let the original side be a units.
Then original volume = a3 cubic units
Now, new side  = 2a units
Then new volume = (2a)3 sq units = 8 a3cubic units
Thus, the volume becomes 8 times the original volume.

Page No 229:

Question 18:

Tick (✓) the correct answer:
If each side of a cube is doubled, its surface area
(a) is doubled
(b) becomes 4 times
(c) becomes 6 times
(d) becomes 8 times

Answer:

(b) becomes 4 times.

Let the side of the cube be a units.
Surface area = 6a2 sq units
Now, new side = 2a units
New surface area = 6(2a2 ) sq units = 24a2 sq units.
Thus, the surface area becomes 4 times the original area.

Page No 229:

Question 19:

Tick (✓) the correct answer:
Three cubes of iron whose edges are 6 cm, 8 cm and 10 cm respectively are melted and formed into a single cube. The edge of the new cube formed is
(a) 12 cm
(b) 14 cm
(c) 16 cm
(d) 18 cm

Answer:

(a) 12 cm

Total volume =63+83+103=216+512+1000=1728 cm3
∴ Edge of the new cube=17283=12 cm

Page No 229:

Question 20:

Tick (✓) the correct answer:
Five equal cubes, each of edge 5 cm, are placed adjacent to each other. The volume of the cuboid so formed, is
(a) 125 cm3
(b) 375 cm3
(c) 525 cm3
(d) 625 cm3

Answer:

(d) 625 cm3

Length of the cuboid so formed = 25 cm
Breadth of the cuboid = 5 cm
Height of the cuboid = 5 cm
∴ Volume of cuboid=25×5×5=625 cm3

Page No 229:

Question 21:

Tick (✓) the correct answer:
A circular well with a diameter of 2 metres, is dug to a depth of 14 metres. What is the volume of the earth dug out?
(a) 32 m3
(b) 36 m3
(c) 40 m3
(d) 44 m3

Answer:

(d) 44 m3

Diameter = 2 m
Radius = 1 m
Height = 14 m
 Volume=πr2h=227×1×1×14=44 m3

Page No 229:

Question 22:

Tick (✓) the correct answer:
If the capacity of a cylindrical tank is 1848 m3 and the diameter of its base is 14 m, the depth of the tank is
(a) 8 m
(b) 12 m
(c) 16 m
(d) 18 m

Answer:

(b) 12 m

Diameter = 14 m
Radius = 7 m
Volume = 1848 m3

Now, volume=πr2h=227×7×7×h=1848 m3 h = 184822×7=12 m

Page No 229:

Question 23:

Tick (✓) the correct answer:
The ratio of the total surface area to the lateral surface area of a cylinder whose radius is 20 cm and height 60 cm, is
(a) 2 : 1
(b) 3 : 2
(c) 4 : 3
(d) 5 : 3

Answer:

(c) 4 : 3

Here, Total surface areaLateral surface area=2πr(h+r)2πrh=h+rh=20+6060=43= 4:3

Page No 229:

Question 24:

Tick (✓) the correct answer:
The number of coins, each of radius 0.75 cm and thickness 0.2 cm, to be melted to make a right circular cylinder of height 8 cm and base radius 3 cm is
(a) 460
(b) 500
(c) 600
(d) 640

Answer:

(d) 640 
Total no. of coins =volume of cylindervolume of each coin=π×3×3×8π×0.75×0.75×0.2=640 



Page No 230:

Question 25:

Tick (✓) the correct answer:
66 cm3 of silver is drawn into a wire 1 mm in diameter. The length of the wire will be
(a) 78 m
(b) 84 m
(c) 96 m
(d) 108 m

Answer:

(b) 84 m
Length=volumeπr22=66×722×0.05×0.05=8400 cm = 84 m

Page No 230:

Question 26:

Tick (✓) the correct answer:
The height of a cylinder is 14 cm and its diameter is 10 cm. The volume of the cylinder is
(a) 1100 cm3
(b) 3300 cm3
(c) 3500 cm3
(d) 7700 cm3

Answer:

(a) 1100 cm3
Volume=πr2h=227×5×5×14=1100 cm3

Page No 230:

Question 27:

Tick (✓) the correct answer:
The height of a cylinder is 80 cm and the diameter of its base is 7 cm. The whole surface area of the cylinder is
(a) 1837 cm2
(b) 1760 cm2
(c) 1942 cm2
(d) 3080 cm2

Answer:

(a) 1837 cm2
Diameter = 7 cm
Radius  =3.5 cm
Height = 80 cm
∴ Total surface area=2πr(r+h)=2×227×3.5(3.5+80)=22(83.5)=1837 cm2

Page No 230:

Question 28:

Tick (✓) the correct answer:
The height of a cylinder is 14 cm and its curved surface area is 264 cm2. The volume of the cylinder is
(a) 308 cm3
(b) 396 cm3
(c) 1232 cm3
(d) 1848 cm3

Answer:

(b) 396 cm3
Here, curved surface area=2πrh=264 cm3
r=264×72×22×14=3 cm
 Volume=πr2h=227×3×3×14=396 cm3

Page No 230:

Question 29:

Tick (✓) the correct answer:
The diameter of a cylinder is 14 cm and its curved surface area is 220 cm2. The volume of the cylinder is
(a) 770 cm3
(b) 1000 cm3
(c) 1540 cm3
(d) 6622 cm3

Answer:

(a) 770 cm3
Diameter = 14 cm
Radius = 7 cm
Now, curved surface area=2πrh=220 cm2
h=220×72×22×7=5 cm
 Volume=πr2h=227×7×7×5=770 cm3

Page No 230:

Question 30:

Tick (✓) the correct answer:
The ratio of the radii of two cylinders is 2 : 3 and the ratio of their heights is 5 : 3. The ratio of their volumes will be
(a) 4 : 9
(b) 9 : 4
(c) 20 : 27
(d) 27 : 20

Answer:

(c) 20:27

We have the following:r1r2=23h1h2=53V1V2=πr12h1πr22h2=2027



Page No 231:

Question 1:

Find the volume of a cube whose total surface area is 384 cm2.

Answer:

Total surface area=6a2
6a2=384
a=3846=8 cm
 Volume=a3=512 cm3

Page No 231:

Question 2:

How many soap cakes each measuring 7 cm × 5 cm × 2.5 cm can be placed in a box of size 56 cm × 40 cm × 25 cm?

Answer:

Volume of a soap cake =7×5×2.5=87.5 cm3
Volume of the box=56×40×25=56000 cm3

No. of soap cakes=5600087.5=640 units

∴ 640 cakes of soap can be placed in a box of the given size.

Page No 231:

Question 3:

The radius and height of a cylinder are in the ratio 5 : 7 and its volume is 550 cm3. Find its radius and height.

Answer:

Radiusheight=rh=57r=57h
Now, volume=πr2h=227×57h×57h×h=550 cm3
 h=550×7×7×722×5×53=7 cmAlso, r=57h=5 cm

Page No 231:

Question 4:

Find the number of coins, 1.5 cm in diameter and 0.2 cm thick, to be melted to form a right circular cylinder with a height of 10 cm and a diameter of 4.5 cm.

Answer:

Volume of the coin=πr2h=227×0.75×0.75×0.2
Volume of the cylinder =πr2h=227×2.25×2.25×10
No. of coins=volume of cylindervolume of coin=2.25×2.25×100.75×0.75×0.2= 450 coins

∴ 450 coins must be melted to form the required cylinder.

Page No 231:

Question 5:

Find the surface area of a chalk box, whose length, breadth and height are 18 cm, 10 cm and 8 cm respectively.

Answer:

Length = 18 cm
Breadth = 10 cm
Height = 8 cm
∴ Total surface area =2lb+lh+bh=218×10+18×8+10×8=2180+144+80=808 cm2  

Page No 231:

Question 6:

The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the diameter and height of the pillar.

Answer:

Curved surface area =2πrh=264 m2
 r=2642πh=132πhm

Volume =πr2h=π×132πh×132πh×h=924 m3
 h=132×132×722×924=6 m

Now, r=132πh=132×722×6=7m

i.e., diameter of the pillar, d=7×2=14 m

Page No 231:

Question 7:

Mark (✓) against the correct answer:
The circumference of the circular base of a cylinder is 44 cm and its height is 15 cm. The volume of the cylinder is
(a) 1155 cm3
(b) 2310 cm3
(c) 770 cm3
(d) 1540 cm3

Answer:

(b) 2310 cm3

Height = 15 cm
Circumference=2πr=44 cm
 r=44×72×22=7 cm
∴ Volume=πr2h=227×7×7×15=2310 cm3

Page No 231:

Question 8:

Mark (✓) against the correct answer:
the area of the base of a circular cylinder is 35 cm2 and its height is 8 cm. The volume of the cylinder is
(a) 140 cm3
(b) 280 cm3
(c) 420 cm3
(d) 210 cm3

Answer:

(b) 280 cm3
Area = 35 cm2
Height = 8 cm
 Volume = base area × height = 35×8=280 cm3

Page No 231:

Question 9:

Mark (✓) against the correct answer:
A cuboid having dimensions 16 m × 11 m × 8 m is melted to form a cylinder of radius 4 m. What is the height of the cylinder?
(a) 28 m
(b) 14 m
(c) 21 m
(d) 32 m

Answer:

(a) 28 m 
Volume of the cuboid=16×11×8=1408 m3
​Volume of the cylinder =πr2h=1408 m3
 h=1408×722×4×4=28 m

Page No 231:

Question 10:

Mark (✓) against the correct answer:
The dimensions of a cuboid are 8 m  6 m  4 m. Its lateral surface area is
(a) 210 m2
(b) 105 m2
(c) 160 m2
(d) 240 m2

Answer:

Lateral surface area =2l+b×h=28+6×4=256=112 m2

Page No 231:

Question 11:

Mark (✓) against the correct answer:
The length, breadth and height of a cuboid are in the ratio 3 : 4 : 6 and its volume is 576 cm3. The whole surface area of the cuboid is
(a) 216 cm2
(b) 324 cm2
(c) 432 cm2
(d) 460 cm2

Answer:

(c) 432 sq cm
Volume=lbh=3x×4x×6x=72x3 =576 cm3
x=576723=2
∴ Total surface area=2lb+bh+lh=2(3x4x+4x6x+3x6x)=2(48+96+72)=432 cm2

Page No 231:

Question 12:

Mark (✓) against the correct answer:
The surface area of a cube is 384 cm2. Its volume is
(a) 512 cm3
(b) 256 cm3
(c) 384 cm3
(d) 320 cm3

Answer:

(a) 512 cm3
Surface area=6a2
6a2=384
a=3846=64=8 cm
∴ Volume=a3=83=512 cm3

Page No 231:

Question 13:

Fill in the blanks.
(i) If l, b, h be the length, breadth and height of a cuboid, then its whole surface area = (.......) sq units.
(ii) If l, b, h be the length, breadth and height of a cuboid, then its lateral surface area = (.......) sq units.
(iii) If each side of a cube is a, then its lateral surface area is ....... sq units.
(iv) If r is the radius of the base and h be the height of a cylinder, then its volume is (.......) cubic units.
(v) If r is the radius of the base and h be the height of a cylinder, then its lateral surface area is (......) sq units.

Answer:

(i) If l, b and h are the length, breadth and height of a cuboid, respectively, then its whole surface area is equal to 2(lb+lh+bh) sq units.
(ii) If l, b and h are the length, breadth and height of a cuboid, respectively, then its lateral surface area is equal to 2((l+b)×h) sq units.
(iii) If each side of a cube is a, then the lateral surface area is 4a2 sq units.
(iv) If r and h are the radius of the base and height of a cylinder, respectively, then its volume is πr2h cubic units.
(v) If r and h are the radius of the base and height of a cylinder, then its lateral surface area is 2πrh sq units.



View NCERT Solutions for all chapters of Class 8