Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: 2007 · Marks: · Difficulty:
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
(b)40
(c)60
(d)80
Answer
Answer (as printed): D
Explanation
Volume of cistern $=\left(\pi \times 10^{2} \times 15\right) \mathrm{m}^{3}=1500 \pi \mathrm{m}^{3}$. Volume of water flowing through the pipe in 1 sec. $$\begin{aligned} & =(\pi \times 0.25 \times 0.25 \times 5) \mathrm{m}^{3}=0.3125 \pi \mathrm{m}^{3} . \\ & \therefore \text { Time taken to fill the cistern }=\left(\frac{1500 \pi}{0.3125 \pi}\right)=\left(\frac{1500 \times 10000}{3125}\right) \\ & =4800 \mathrm{sec}=\left(\frac{4800}{60}\right) \mathrm{min}=80 \mathrm{min} . \end{aligned}$$