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

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3 hr

2 hr

5 hr

10 hr

answer is B.

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Detailed Solution

Given that the speed of the water is 15km/h through a pipe having a diameter

d = 14

cm into a cuboidal pond, which is,

l = 50

m and 44 m wide.
The volume of the water flowing out of the pipe in 1 hour:
Let us suppose the level of the water in the pond rises by

l = 21 c m

in t hours.
So, the radius of the pipe is,

n × π r 2 h = 23 π r 3 n × 1.5 2 × 4 = 23 × 93 n = 2 × 9 × 9 × 9 1.5 × 1.5 × 3 × 4 n = 54

Now, calculating the volumetric flow of the water flowing out of the pipe in 1 hour is:

V = π r 2 h V = π 7 cm 2 15 km / hr V = 3.14 0.049 m 2 15000 m / hr V = 231 m 3 / hr

The volume of the water flowing out of the pipe in

r 2 = 8

hr is,

V = 231 t m 3

.
Now, the volume of the water in the cuboidal pond and the time in which the level of the water rises to 21 cm. We get,

V = 13 π h r 1 2 + r 2 2 + r 1 r 2 V = 13 × 227 × 16 × 202 + 82 + 208 V = 22 × 16 × 624 21 V = 10459.43 c m 3

The volume of the water flowing out of the pipe in t hours = the volume of the water in the cuboidal pond. So,

V = V c 231 t = 462 t = 462231 t = 2 hr

Therefore, 2 is the correct option.

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