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A cylindrical water tank of diameter $1.4 m$ and height $2.1 m$ is being fed by a pipe of diameter $3.5 cm$ through which water flows at the rate of 2 meter per second. In how much time the tank will be filled?

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28 minutes

45 minutes

23 minutes

65 minutes

answer is A.

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Detailed Solution

It is given a cylindrical water tank of diameter 1.4 m, height 2.1 m and a pipe of diameter 3.5 cm through which water flows at the rate of 2 meter per second.
We know that, 1 m = 100

cm

.
Diameter of pipe is,

d = 3.5 cm ⇒ d = 3.5 100 m

So, radius =

D i a m e t e r 2

(r 1) = 3.5 2 × 100 ⇒ (r 1) = 1.75 100 m

(r 2) = 1.4 2 ⇒ (r 2) = 0.7 m

We know that, volume of cylinder =

π r 2 h

So, volume

(V 1) = π r 1 2 h 1

⇒ V 1 = 227 × 1.75 100 2 × 2

⇒ V 1 = 227 × 1.75 100 × 1.75 100 × 2

⇒ V 1 = 19251000000 m 3

Volume

(V 2) = π r 2 2 h 2

⇒ V 2 = 227 × 0.7 2 × 2.1

⇒ V 2 = 227 × 710 × 710 × 2110

⇒ V 2 = 32341000 m 3

T i m e = V 2 V 1

⇒ T i m e = 32341000 ÷ 19251000000

⇒ T i m e = 32341000 ÷ 19251000000

⇒ T i m e = 32341000 × 10000001925

⇒ T i m e = 1680 s

⇒ T i m e = 168060

minutes (1minute=60s)

⇒ T i m e =

28 minutes
Therefore, the tank will be filled in 28 minutes.
Hence option (1) is correct.

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