Water flows at the rate of 10 metre per minute 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 sec
(b) 51 minutes 12 sec
(c) 52 minutes 1 sec
(d) 55 minutes
The radius of cylindrical pipe
$r=5 / 2 \mathrm{~mm}=0.25 \mathrm{~cm}$
The volume per minute of water flow from the pipe
$=\pi \times(0.25)^{2} \times 1000$
$=62.5 \pi \mathrm{cm}^{3} /$ minute
The radius of cone
$=\frac{40}{2}$
$=20 \mathrm{~cm}$
Depth of cone = 24 cm
The volume of cone
$=3200 \pi \mathrm{cm}^{3}$
The time it will take to fill up a conical vessel
$=51 \frac{125}{625} \mathrm{~min}$
$=51 \mathrm{~min}+\frac{125}{625} \times 60 \mathrm{sec}$
$=51 \mathrm{~min}+12 \mathrm{sec}$
Hence, the correct answer is choice (b).