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Water flows at the rate of 10 m per min from cylindrical pipe 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40 cm and depth 24 cm ?

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48 min 15 sec

51 min 12 sec

52 min 1 sec

55 min

answer is B.

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Detailed Solution

Given,
r = Radius of the base of the conical vessel = 20 cm
h = Height of the conical vessel = 24 cm
Radius of pipe

= \frac{5}{2} mm

\Rightarrow 2.5 mm

\Rightarrow \frac{25}{100} cm

[1mm =

\frac{1}{100}

cm]
Volume of the conical vessel

= \frac{1}{3} π r^{2} h

\Rightarrow \frac{1}{3} \times \frac{22}{7} \times 20 \times 20 \times 24

Suppose the conical vessel is filled in 1 minutes.
Then, Length of the water column

= (10 \times 1) m

\Rightarrow 1000 cm

Here, height is considered as the distance travelled.
Since the pipe is cylindrical in shape, Volume

= π {(Radius)}^{2} \times h eig h t

Volume of the water that flows in 1 minutes

= \frac{22}{7} \times (\frac{25}{100})^{2} \times 1000 c m^{3}

Now, time taken to fill the cistern

= \frac{Volum e of t h e vessel}{Volume of water coming out of pipe in one minute}

\Rightarrow \frac{\frac{1}{3} π \times 20 \times 20 \times 24}{π \times \frac{25}{100} \times \frac{25}{100} \times 1000}

\Rightarrow 51 \frac{1}{5} minutes

(1 min = 60 sec)

\Rightarrow 51 \min 12 \sec

Therefore, the conical vessel is filled in

51 \min 12 \sec

.
Hence, the correct option is 2.

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