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## Chapter 13: Surface Areas and Volumes

#### TEXTBOOK’S EXERCISE – 13.5

1. A matchbox measures 4 cm × 2.5 cm × 1.5 cm. What will be the volume of a packet containing 12 such boxes?

Sol. Here, l = 4 cm, b = 2.5 cm, h = 1.5 cm

Volume of 1 matchbox

= lbh = 4 × 2.5 × 1.5 cm3 = 15 cm3

Volume of 12 matchboxes

= 15 × 12 cm3 = 180 cm3

2. A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many litres of water can it hold? (1 m3 = 1000 l)

Sol. Here, l = 6 m, b = 5 m, h = 4.5 m

Volume of the tank = lbh

= 6 × 5 × 4.5 m3 = 135 m3

= 135 × 1000 litres = 1,35,000 litres. (Since 1 m3 = 1000 litres)

Hence, the tank can hold 1,35,000 litres of water.

3. A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?

Sol. Here, l = 10 m, b = 8 m, h = ?

The volume of the vessel = lbh

⇒ 380 = 10 × 8 × h

Hence, the tank must be made 4.75 m high

#### TEXTBOOK’S EXERCISE – 13.5

4. Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of Rs 30 per m3.

Sol. l = 8 m, b = 6 m, h = 3 m

The volume of the pit

= lbh = 8 × 6 × 3 m3 = 144 m3

Cost of digging 1m3 = Rs 30

∴ Cost of digging 144 m3 = Rs 30 × 144

= Rs 4320

5. The capacity of a cuboidal tank is 50000 litres of water. Find the breadth of the tank, if its length and depth are respectively 2.5 m and 10 m.

Sol. Here, l = 2.5 m, h = 10 m, b = ?

The capacity of the tank

Also, the capacity of the tank = lbh

⇒ 50 = 2.5 × b × 10 ⇒ b = 50 25 = 2

Hence, the breadth of the tank = 2 m

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