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## Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 7 Mensuration Ex 7.3

Question 1.

Find the volume of a cuboid whose dimensions are

(i) length = 12 cm, breadth = 8 cm, height = 6 cm

(ii) length = 60 m, breadth = 25 m, height = 1.5 m

Solution:

(i) l = 12 cm

b = 8 cm

h = 6 cm

Volume of the cuboid = lbh

= 12 × 8 × 6 cm^{3} = 576 cm^{3}

(ii) l = 60 m

b = 25 m

h = 1.5 m

Volume of the cuboid = lbh = 60 × 25 × 1.5m^{3} = 2250 m^{3}

Question 2.

The dimensions of a match box are 6 cm × 3.5 cm × 2.5 cm. Find the volume of a packet containing 12 such match boxes.

Solution:

Dimensions of a match box = 6 cm × 3.5 cm × 2.5 cm

V = (6 × 3.5 × 2.5) cm^{3} = 52.5 cm^{3}

Volume of 12 such boxes = 12 × 52.5 cm^{3} = 630 cm^{3}

Question 3.

The length, breadth and height of a chocolate box are in the ratio 5 : 4 : 3. If its volume is 7500 cm^{3}, then find its dimensions.

Solution:

Let 1 ratio = x then 5 : 4 : 3

x = 5 cm

∴ 5x = 5 × 5 = 25 cm

4x = 4 × 5 = 20 cm

3x = 3 × 5 = 15 cm

∴ Dimensions of a chocolate box are 25 cm × 20 cm × 15 cm

Question 4.

The length, breadth and depth of a pond are 20.5 m, 16 m and 8 m respectively. Find the capacity of the pond in litres.

Solution:

l = 20.5 m

b = 16 m

h = 8 m

∴ Capacity = Volume = lb h = (20.5 × 16 × 8) m^{3} = 2624 m^{3}

1 m^{3} = 1000 litres

∴ 2624 m^{3} = 2624000 litres

Question 5.

The dimensions of a brick are 24 cm × 12 cm × 8 cm. How many such bricks will be required to build a wall of 20 m length, 48 cm breadth and 6 m height?

Solution:

l = 24 cm

b = 12 cm

h = 8 cm

Volume of the brick = lbh = (24 × 12 × 8) cm^{3} = 2304 cm^{3}

Wall dimensions are :

L = 20 m = 2000 cm

B = 48 cm

H = 6 m = 600 cm

No. of bricks required = 25000

Question 6.

The volume of container is 1440 m^{3}. The length and breadth of the container are 15 m and 8 m respectively. Find its height.

Solution:

V = l × b × h = 1440 m^{3}

15 × 8 × h = 1440

Question 7.

Find the volume of a cube each of whose side is

(i) 5 cm

(ii) 3.5 m

(iii) 21 cm

Solution:

(i) side of a cube (a) = 5 cm

Volume of a cube V = a^{3} = 5 × 5 × 5 = 125 cm^{3}

(ii) a = 3.5 m

V = a^{3} = 3.5 × 3.5 × 3.5 m^{3} = 42.875 m^{3}

(iii) a = 21 cm 23 = 21 × 21 × 21 cm^{3} = 9261 cm^{3}

Question 8.

A cubical milk tank holds 125000 litres of milk. Find the length of its side in metres.

Solution:

V = a^{3} = 125000 litres = 125 m^{3}

∴ length of its side = 5 m.

Question 9.

A metallic cube with side 15 cm is melted and formed into a cuboid. If the length and height of the cuboid is 25 cm and 9 cm respectively then find the breadth of the cuboid.

Solution:

The volume of the cuboid formed = The volume of the cube melted.

height of the cuboid = 15 cm