Question

The rain water from a roof of 44 m $\times$ 20 m drains into a cylindrical tank having diameter of base 4 m and height 3.5 m. If the tank is just full, then find the rainfall in cm. [CBSE 2014]

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{roof},l=44\mathrm{m}, \\ \mathrm{the}\mathrm{width}\mathrm{of}\mathrm{the}\mathrm{roof},b=20\mathrm{m}, \\ \mathrm{the}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{cylindrical}\mathrm{tank},H=3.5\mathrm{m}\mathrm{and} \\ \mathrm{the}\mathrm{base}\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{cylindrical}\mathrm{tank},R=\frac{4}{2}=2\mathrm{m} \\ \mathrm{Let}\mathrm{the}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{rainfall}\mathrm{be}h. \\ \mathrm{Now}, \\ \mathrm{Volume}\mathrm{of}\mathrm{rainfall}=\mathrm{Volume}\mathrm{of}\mathrm{cylindrical}\mathrm{tank} \\ \Rightarrow lbh=\mathrm{\pi }{R}^{2}H \\ \Rightarrow 44\times 20\times h=\frac{22}{7}\times 2\times 2\times 3.5 \\ \Rightarrow h=\frac{22}{7}\times \frac{2\times 2\times 3.5}{44\times 20} \\ \Rightarrow h=\frac{1}{20}\mathrm{m} \\ \Rightarrow h=\frac{100}{20}\mathrm{cm} \\ \therefore h=5\mathrm{cm} \end{gathered}$$

So, the height of the rainfall is 5 cm.