Question

The rain water from a roof $22m$ by $20m$ drains into a conical vessel having the diameter of base as $2m$ and height $3.5m$. If the vessel is just full, find the rainfall in mm.

Answer 1

Total rain fall $=$ Volume of vessel

$=\frac{1}{3}\times \pi \times {\left(\frac{2}{2}\right)}^2\times 3.5$

$=\frac{3.5\pi }{3}{m}^3$

$=$ Area of roof $\times$ height of rainfall

$\Rightarrow \frac{3.5\pi }{3}=22\times 20\times h$

$\Rightarrow R=\frac{3.5\pi }{3\times 22\times 20}m=\frac{3.5\pi \times 1000}{3\times 22\times 20}mm$

$=\frac{7\times 22\times 1000}{7\times 6\times 22\times 20}=\frac{50}{6}mm=8.33mm$