Question

The lateral area of a right cylindrical tank is 48πm2

 and its volume is 72πm3.

 Find the altitude of the tank.

Answer 1

The lateral area is given by $S=2\pi r h$ while his volume is given by $V=\pi r^2 h$. We remark that the ratio $\frac{S^2}{V}= \frac{4\pi^2 r^2 h^2}{\pi r^2 h}=4\pi h$. This gives us $h=\frac{S^2}{4\pi V}=\frac{48^2 \pi^2}{4\pi^2\cdot 72}=8m$