Water flows at the rate of 10 metres per minutes from a 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 ?

A. 48 minutes 15 seconds

B. 51 minutes 12 seconds

C. 52 minutes 1 seconds

D. 55 minutes

Answer: Option B

Solution(By Examveda Team)

Volume flown in conical vessel :
$$\eqalign{ & = \frac{1}{2}\pi \times {\left( {20} \right)^2} \times 24 \cr & = 3200\pi \cr} $$
Volume flown in 1 minute :
$$\eqalign{ & = \left( {\pi \times \frac{{2.5}}{{10}} \times \frac{{2.5}}{{10}} \times 1000} \right) \cr & = 62.5\pi \cr} $$
∴ Time taken :
$$\eqalign{ & = \left( {\frac{{3200\pi }}{{62.5\pi }}} \right) \cr & = 51\operatorname{minutes} 12\operatorname{seconds} \cr} $$