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#### TEXTBOOK’S EXERCISE – 13.5

6. A village, having a population of 4000, requires 150 litres of water per head per day. It has a tank meas­uring 20 m × 15 m × 6 m. For how many days will the water of this tank last?

Sol. Here, l = 20 m, b = 15 m, h = 6 m

The population of the village = 4000

Water consumed by 1 person in 1 day

= 150 litres

∴ Water consumed by 4000 persons in 1 day

= 4000 × 150 litres

Also, the capacity of the tank

= lbh = 20 × 15 × 6 m3

∴ Required number of days

Hence, the water of this tank will last for 3 days.

7. A godown measures 40 m × 25 m × 10 m. Find the maximum number of wooden crates each measuring 1.5 m × 1.25 m × 0.5 m that can be stored in the godown.

Sol. The volume of the godown = 40 × 25 × 10 m3

Volume 1 wooden crate = 1.5 × 1.25 × 0.5 m3

∴ Required number of crates

Hence, the maximum number of wooden crates that can be stored in the godown = 10666

8. A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.

Sol. Here, a = 12 cm

Volume of the cube = a3 = (12)3 cm3

= 1728 cm3 . Now, the volume of 1 smaller cube

Let, the side of the new cube is A.

Then A3 = 216

Hence, the side of the new cube = 6 cm

The total surface area of the bigger cube = 6 a2

= 6 × (12)2 cm2 = 6 × 12 × 12 cm2

The total surface area of 1 smaller cube

= 6A2 = 6 × 62 cm2 = 6 × 6 × 6 cm2

Hence, the required ratio

9. A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?

Sol. Here, b = 40 m, h = 3 m, l = 2 km = 2000 m

The volume of water flowing through the river in 1 hour = lbh = 2000 × 40 × 3 m3

∴ The volume of water flowing through the river in 1 minute

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