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A rectangular water reservoir is $10.8 m$ by $3.75 m$ at the base. Water flows into it at the rate of $18 m / s$ through a pipe having the cross section $7.5 cm × 4.5 cm .$ Find the height to which the water will rise in the reservoir in 30 minutes.

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9.2m

4.8m

3.2m

2.7m

answer is D.

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Detailed Solution

Given a rectangular water reservoir with base 10.8 m by 3.75 m. Water flows into it at the rate of 18m/s through a pipe having the cross-section 7.5 cm x 4.5 cm.
Let the water is raised by the height h.
The volume of the cuboid is

V = l × b × h

.
Then the volume of the rectangular water reservoir is,

V = l × b × h ⇒ V = 10.8 × 3.75 × h ⇒ V = 40.5 h m 3 .... (1)

Also, the cross section of pipe is,

⇒ 7 .5 × 4 .5 ⇒ 33.75 cm 2 ⇒ 0.003375 m 2

The distance covered by the water.

Distance = speed ​ ​ × ​ ​ time ⇒ Distance = 18 × 30 × 60 ⇒ Distance = 32400 m

The volume of the water flowed in 30 minutes is,

⇒ Cross section of pipe × distance covered ⇒ 0.003375 × 32400 ⇒ 109.35 m 3

Therefore, by the equation (1),

⇒ 40.5 h = 109.35 ⇒ h = 109.35 40.5 ⇒ h = 2.7 m

Thus, the height to which the water will rise in the reservoir in 30minutes is 2.7m.
Therefore, option (4) is correct.

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