# Water flows at the rate of 10 metres per minute through a cylindrical pipe 5 mm in diameter.

Question:

Water flows at the rate of 10 metres per minute through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter art the surface 40 cm and depth 24 cm?

Solution:

Radius of the cylindrical pipe = 2.5 mm = 0.25 cm
Water flowing per minute = 10 m = 1000 cm

Volume of water flowing per minute through the cylindrical pipe $=\pi(0.25)^{2} 1000 \mathrm{~cm}^{3}=196.4 \mathrm{~cm}^{3}$

Radius of the the conical vessel = 40 cm
Depth of the vessel = 24 cm

Volume of the vessel $=\frac{1}{3} \pi(20)^{2} 24=10057.1 \mathrm{~cm}^{3}$

Let the time taken to fill the conical vessel be x min.

Volume of water flowing per minute through the cylindrical pipe  x = volume of the conical vessel

$\Rightarrow x=\frac{10057.1}{196.4}=51 \min 12 \sec$

∴ The cylindrical pipe would take 51 min 12 sec to fill the conical vessel.