Mathematics Solutions Solutions for Class 8 Math Chapter 1 Rational And Irrational Numbers are provided here with simple step-by-step explanations. These solutions for Rational And Irrational Numbers are extremely popular among Class 8 students for Math Rational And Irrational Numbers Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Mathematics Solutions Book of Class 8 Math Chapter 1 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Mathematics Solutions Solutions. All Mathematics Solutions Solutions for class Class 8 Math are prepared by experts and are 100% accurate.

#### Question 1:

Find the volume of a box if its length, breadth and height are 20 cm, 10.5 cm and 8 cm respectively.

#### Question 2:

A cuboid shape soap bar has volume 150 cc. Find its thickness if its length is 10 cm and breadth is 5 cm.

Volume of soap bar = 150 cc

#### Question 3:

How many bricks of length 25 cm, breadth 15 cm and height 10 cm are required to build a wall of length 6 m, height 2.5 m and breadth 0.5 m?

Let the number of bricks required be n.
Volume of each brick =
Volume of the wall =
Number of bricks required(n) =
Thus, 2000 bricks are required to make the wall.

#### Question 4:

For rain water harvesting a tank of length 10 m, breadth 6 m and depth 3 m is built. What is the capacity of the tank? How many litre of water can it hold?

length = 10 m
depth = 3 m
Volume of the tank =

#### Question 1:

In each example given below, radius of base of a cylinder and its height are given. Then find the curved surface area and total surface area.
(1) r = 7 cm, h = 10 cm
(2) r = 1.4 cm, h = 2.1 cm
(3) r = 2.5 cm, h = 7 cm
(4) r = 70 cm, h = 1.4 cm
(5) r = 4.2 cm, h = 14 cm

We know that
Curved surface area of a cylinder = $2\mathrm{\pi }rh$
Total surface area = $2\mathrm{\pi }r\left(h+r\right)$
(1) r = 7 cm, h = 10 cm
Curved surface area of a cylinder = $2\mathrm{\pi }rh$ = $2\mathrm{\pi }×7×10=140\mathrm{\pi }=140×\frac{22}{7}=440$ sq cm
Total surface area = $2\mathrm{\pi }r\left(h+r\right)$ = $2×\frac{22}{7}×7\left(10+7\right)=748$ sq cm
(2) r = 1.4 cm, h = 2.1 cm
Curved surface area of a cylinder = $2\mathrm{\pi }rh$ = $2×\frac{22}{7}×1.4×2.1=18.48$ sq cm
Total surface area = $2\mathrm{\pi }r\left(h+r\right)$ = $2×\frac{22}{7}×1.4\left(2.1+1.4\right)=30.8$ sq cm
(3) r = 2.5 cm, h = 7 cm
Curved surface area of a cylinder = $2\mathrm{\pi }rh$ = $2×\frac{22}{7}×2.5×7=110$ sq cm
Total surface area = $2\mathrm{\pi }r\left(h+r\right)$ = $2×\frac{22}{7}×2.5\left(2.5+7\right)=149.28$ sq cm
(4) r = 70 cm, h = 1.4 cm
Curved surface area of a cylinder = $2\mathrm{\pi }rh$ = $2×\frac{22}{7}×70×1.4=616$ sq cm
Total surface area = $2\mathrm{\pi }r\left(h+r\right)$ = $2×\frac{22}{7}×70\left(70+1.4\right)=31416$ sq cm
(5) r = 4.2 cm, h = 14 cm
Curved surface area of a cylinder = $2\mathrm{\pi }rh$ = $2×\frac{22}{7}×4.2×14=369.6$ sq cm
Total surface area = $2\mathrm{\pi }r\left(h+r\right)$ = $2×\frac{22}{7}×4.2\left(4.2+14\right)=480.48$ sq cm

#### Question 2:

Find the total surface area of a closed cylindrical drum if its diameter is 50 cm and height is 45 cm. (π = 3.14)

Diameter = 50 cm
Height = 45 cm
Total surface area = $2\mathrm{\pi }r\left(h+r\right)$

Thus, the total surface area of the closed cylinderical drum is 10990 sq cm.

#### Question 3:

Find the area of base and radius of a cylinder if its curved surface area is 660 sqcm and height is 21 cm.

Curves surface area = 660 sq cm
Height = 21 cm
Curved surface area = $2\mathrm{\pi }rh=2×\frac{22}{7}×r×21=660\phantom{\rule{0ex}{0ex}}$

Area of base =

#### Question 4:

Find the area of the sheet required to make a cylindrical container which is open at one side and whose diameter is 28 cm and height is 20 cm. Find the approximate area of the sheet required to make a lid of height 2 cm for this container.

Diameter = 28 cm
Height = 20 cm
Curved surface area of the cylinder + area of the base = area of the sheet

Thus, area of sheet required = 2376 cm
Area of sheet required to make a lid of height 2 cm will be

Thus, area of sheet used to make the lid is 792 sq cm.

#### Question 1:

Find the volume of the cylinder if height (h) and radius of the base (r) are as given below.
(1) r = 10.5 cm, h =8 cm
(2) r = 2.5 m, h = 7 m
(3) r = 4.2 cm, h = 5 cm
(4) r = 5.6 cm, h = 5 cm

Volume of the cylinder = $\mathrm{\pi }{r}^{2}h$
(1) r = 10.5 cm, h =8 cm
Volume = $\mathrm{\pi }{r}^{2}h$$\frac{22}{7}×10.5×10.5×8=2772$ cubic cm
(2) r = 2.5 m, h = 7 m
Volume = $\mathrm{\pi }{r}^{2}h$ = $\frac{22}{7}×2.5×2.5×7=137.5$ cubic cm
(3) r = 4.2 cm, h = 5 cm
Volume = $\mathrm{\pi }{r}^{2}h$ = $\frac{22}{7}×4.2×4.2×5=277.2$ cubic cm
(4) r = 5.6 cm, h = 5 cm
Volume = $\mathrm{\pi }{r}^{2}h$ = $\frac{22}{7}×5.6×5.6×5=492.8$ cubic cm

#### Question 2:

How much iron is needed to make a rod of length 90 cm and diameter 1.4 cm?

Total length = 90 cm
Diameter = 1.4 cm
Total iron required = Volume of cylinder
$\mathrm{\pi }{r}^{2}h=\frac{22}{7}×0.7×0.7×90=138.6$ cm
Thus, 138.6 cmof iron is required.

#### Question 3:

How much water will a tank hold if the interior diameter of the tank is 1.6 m and its depth is 0.7 m?

Diameter = 1.6 m
Depth = 0.7 m
Volume of the tank = ${\mathrm{\pi r}}^{2}\mathrm{h}=\frac{22}{7}×{\left(0.8\right)}^{2}×0.7=1.408$ m3.

Thus, the tank will hold 1408 L.

#### Question 4:

Find the volume of the cylinder if the circumference of the cylinder is 132 cm and height is 25 cm.

Volume = $\mathrm{\pi }{r}^{2}h=\frac{22}{7}×21×21×25=34650$ cm3