Water flows at the rate of 10 metre per minute

Solution:

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).