Mathematics Semester i Solutions Solutions for Class 7 Math Chapter 8 Mensuration are provided here with simple step-by-step explanations. These solutions for Mensuration are extremely popular among class 7 students for Math Mensuration Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Mathematics Semester i Solutions Book of class 7 Math Chapter 8 are provided here for you for free. You will also love the ad-free experience on Meritnationâ€™s Mathematics Semester i Solutions Solutions. All Mathematics Semester i Solutions Solutions for class 7 Math are prepared by experts and are 100% accurate.

#### Page No 107:

#### Question O1:

How many identical square surfaces are there in a cube?

#### Answer:

In a cube, there are six identical square surfaces.

#### Page No 107:

#### Question W1:

Calculate the total surface areas of cubes whose edges are

(1) 8 cm

(2) 12 cm

(3)

(4) 1.5 m

#### Answer:

(1) We have:

Total surface area of the cube:

(2)

We have:

Total surface area of the cube:

(3) We have:

Total surface area of the cube:

(4) We have:

Total surface area of the cube:

#### Page No 107:

#### Question O2:

State any two differences between plane figures and solid figures.

#### Answer:

(i) Plane figures have two dimensions**-** length and breadth, whereas solid figures have three dimensions**-** length, breadth and height.

(ii) Plane figures have no volume, whereas solid figures have a volume.

#### Page No 107:

#### Question W2.1:

The total surface area of a cubical die is 24 cm^{2}. Find the length of each edge?

#### Answer:

Thus, the length of each edge of the cube is 2 cm.

#### Page No 107:

#### Question W2.2:

The total surface area of a cubical chalk box is 96 cm^{2}. What is the length of its edge?

#### Answer:

Thus, the length of each edge of the cubical chalk box is 4 cm.

#### Page No 107:

#### Question W2.3:

The edge of a cubical room is 3 m. The inner walls are to be painted (inclusive of windows and doors). Find the expenditure to be incurred at the rate of Rs 15/- per square metre.

#### Answer:

Total surface area of the inner walls of the cubical room:

Cost of painting per 1 m^{2} of area = Rs.15

∴Amount required for painting the inner walls =

#### Page No 107:

#### Question O3:

What is the formula to find the total surface area of a cube?

#### Answer:

The formula to find the total surface area of a cube is , where *a* is the side of the cube.

#### Page No 110:

#### Question O1:

Give two examples for a cuboid.

#### Answer:

Book and brick are two examples of a cuboid.

#### Page No 110:

#### Question W1:

A rectangular chalk box has a length 16 cm, breadth 8 cm and height 5 cm. Find its total surface area.

#### Answer:

We have:

#### Page No 110:

#### Question O2:

How many edges a cuboid has?

#### Answer:

A cuboid has 12 edges.

#### Page No 110:

#### Question W2:

Find the area of card board required to make a closed box of length 25 cm, breadth 10.5 cm and height 15 cm.

#### Answer:

We have:

Thus, 1590 cm^{2} of card board is required to make the box.

#### Page No 110:

#### Question W3:

The length, breadth and height of a room are 11 m, 8 m and 5 m respectively. Find the surface area of its 4 walls and the floor (inclusive of doors and windows).

#### Answer:

We have:

The surface area of the 4 walls and the floor:

#### Page No 110:

#### Question O3:

Give the formula to find the total surface area of a cuboid.

#### Answer:

The formula to find the total surface area of a cuboid is , where *l* is the length, *b* is the breadth and *h* is the height of the cuboid.

#### Page No 110:

#### Question W4:

The length, breadth and the height of a tin box are 26 cm, 26 cm and 45 cm respectively. Find the area of tin required to make 30 such boxes. If the cost of tin per square metre is Rs 80/-, find the amount required to make 30 boxes.

#### Answer:

We have:

∴ TSA of 30 tin boxes =

Cost of 1 m^{2} of the tin = Rs.80

∴Cost of 18.096 m^{2} =Rs.

Thus, Rs.1447.68 are required to make 30 boxes.

#### Page No 111:

#### Question W5:

The inner perimeter of a rectangular room is 250 m. Its height is 6 m. What is the amount to be spent to paint the walls of the room at the rate of Rs 12/- per square metre. (inclusive of doors and windows)

#### Answer:

The inner perimeter of a rectangular room is 250 m.

Surface area of the 4 walls =

Cost of painting an area of 1 m^{2} = Rs.12

∴Cost of painting the area of 1500 m^{2} =

Thus, Rs.18000 are required to paint the walls of the room.

#### Page No 118:

#### Question O1:

What is the volume?

#### Answer:

Volume of an object is the capacity of the object. It also refers to the space occupied by the object or the size of the object.

#### Page No 118:

#### Question O2:

What is the volume of a box whose length is 3 cm, breadth is 3 cm and height is 3 cm?

#### Answer:

37 cm^{3}

#### Page No 118:

#### Question O3:

What is the formula to find the volume of a cube?

#### Answer:

Volume of a cube is given by , where *l* is the length of the side of the cube.

#### Page No 119:

#### Question W1:

The measurements of some cuboids are as follows. (Complete the given table).

#### Answer:

**Explanation: **

(i) Length = 4 cm, breadth = 3 cm, height = 5 cm

Volume = *lbh *= (4 × 3 × 5) cm^{3} = 60 cm^{3}

(ii) Length = 2 cm, breadth = 6 cm, height = 8 cm

Volume = *lbh *= (2 × 6 × 8) cm^{3} = 96 cm^{3}

(iii) Length = 7 cm, breadth = 3 cm, height = 4 cm

Volume = *lbh *= (7 × 3 × 4) cm^{3} = 84 cm^{3}

(iv) Length = 12 cm, breadth = 9 cm, height = 12 cm

Volume = *lbh *= (12 × 9 × 12) cm^{3} = 1296 cm^{3}

(v) Length = 16 cm, breadth = 14 cm, height = 18 cm

Volume = *lbh *= (16 × 14 × 18) cm^{3} = 4032 cm^{3}

(vi) Length = ?, breadth = 28 cm, height = 24 cm, volume = 26880

Volume = *lbh *

(vii) Length = 40, breadth = 24 cm, height = ?, volume = 2400

Volume = *lbh *

(viii) Length = 60, breadth = ?, height = 5, volume = 5400

Volume = *lbh *

#### Page No 119:

#### Question W2:

Find the volumes of cubes whose edges are

(1) 2 m

(2) 5 cm

(3) 8 cm

#### Answer:

(a) We have:

Volume of cube

(b) We have:

Volume of cube

(c) We have:

Volume of cube =

#### Page No 119:

#### Question W3:

Find the length of edges of cubes whose volumes are

(a) 216 c.c

(b) 2,197 c.c

#### Answer:

(a) We have:

Thus, the length of the edge of the cube is 6 cm.

(b) We have:

Thus, the length of the edge of the cube is 13 cm.

#### Page No 119:

#### Question W4.1:

The volume of a cuboidal soap is 150 c.c. The length is 10 cm and breadth is 5 cm. Find its height.

#### Answer:

So, the height of the cuboid is 3 cm.

#### Page No 119:

#### Question W4.2:

A platform of the following dimensions is to be constructed-length 24 m, breadth 6 m and height 0.4 m. How many bricks of dimensions 25 cm, 16 cm and 10 cm are required to construct the platform.

#### Answer:

Volume of the platform,

Volume of one brick,

Thus, the required number of bricks:

#### Page No 119:

#### Question W4.3:

How many cubes of length 3 cm can be made from the cubical wood piece of length 30 cm.

#### Answer:

Volume of the bigger cube:

Volume of the smaller cube:

Thus, the number of bricks that can be formed:

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