ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.5 in Chapter 17 - Mensuration

Question 29 Mensuration Exercise 17.5

Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboid pond which is 50 m long and 44 m wide. In what time will the level of water in the pond rise by 21 cm?

Solution:

Here the volume of water in pipe is equal to the volume of water transferred to the pond which results in increase of water level in the pond.

Given speed of water flow = 15 km/h

Diameter of pipe = 14 cm

So radius of pipe, r = 14/2 = 7 cm = 0.07 m

Dimensions of cuboidal pond = 50 m × 44 m

Height of water in pond = 21 cm = 0.21 m

So volume of water in pond = 50×44 ×0.21

= 462 m3

Volume of water in pipe = π r2h

= π x 0.072×h

= 0.0049h

Volume of water in pond = Volume of water in pipe

462 = 0.0049h

h = 462/0.0049

= 462×7/0.0049×22

= 30000 m

= 30 km, (1 km = 1000 m)

Speed = distance/ time

Time = Distance/speed = 30/15 = 2 hr

Hence the time taken is 2 hours.

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