Question
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 ?
Answer: Option D
Volume of cistern :
$$\eqalign{
& = \left( {\pi \times {{10}^2} \times 15} \right){m^3} \cr
& = 1500\pi {m^3} \cr} $$
Volume of water flowing through the pipe in 1 sec :
$$\eqalign{
& = \left( {\pi \times 0.25 \times 0.25 \times 5} \right){m^3} \cr
& = 0.3125\pi {m^3} \cr} $$
∴ Time taken to fill the cistern :
$$\eqalign{
& = \left( {\frac{{1500\pi }}{{0.3125\pi }}} \right) \cr
& = \left( {\frac{{1500 \times 10000}}{{3125}}} \right) \cr
& = 4800\,\sec \cr
& = \left( {\frac{{4800}}{{60}}} \right)\min \cr
& = 80\,\min \cr} $$
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Volume of cistern :
$$\eqalign{
& = \left( {\pi \times {{10}^2} \times 15} \right){m^3} \cr
& = 1500\pi {m^3} \cr} $$
Volume of water flowing through the pipe in 1 sec :
$$\eqalign{
& = \left( {\pi \times 0.25 \times 0.25 \times 5} \right){m^3} \cr
& = 0.3125\pi {m^3} \cr} $$
∴ Time taken to fill the cistern :
$$\eqalign{
& = \left( {\frac{{1500\pi }}{{0.3125\pi }}} \right) \cr
& = \left( {\frac{{1500 \times 10000}}{{3125}}} \right) \cr
& = 4800\,\sec \cr
& = \left( {\frac{{4800}}{{60}}} \right)\min \cr
& = 80\,\min \cr} $$
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