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1. The radius of a cylindrical cistern is 10 metres and its height is 15 metres. Initially the cistern is empty. We start filling the cistern with water through a pipe whose diameter is 50 cm. Water is coming out of the pipe with a velocity of 5 m/sec. How many minutes will it take in filling the cistern with water ?

A. 20 min

B. 40 min

C. 60 min

D. 80 min

Solution:

Volume of cistern :

\begin{aligned} = (π \times 10^{2} \times 15) m^{3} \\ = 1500 π m^{3} \end{aligned}

Volume of water flowing through the pipe in 1 sec :

\begin{aligned} = (π \times 0.25 \times 0.25 \times 5) m^{3} \\ = 0.3125 π m^{3} \end{aligned}

∴ Time taken to fill the cistern :

\begin{aligned} = (\frac{1500 π}{0.3125 π}) \\ = (\frac{1500 \times 10000}{3125}) \\ = 4800 \sec \\ = (\frac{4800}{60}) min \\ = 80 min \end{aligned}

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