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?

Answer 1

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 = $\mathrm{\pi }(0.25{)}^{2}1000{\mathrm{cm}}^3$ = 196.4 cm³
Radius of the the conical vessel = 40 cm
Depth of the vessel = 24 cm
Volume of the vessel = $\frac{1}{3}\mathrm{\pi }(20{)}^{2}24=10057.1{\mathrm{cm}}^3$
Let the time taken to fill the conical vessel be x min.
Volume of water flowing per minute through the cylindrical pipe $\times$ 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.