Question

The ratio between the base radius and the height of a solid right circular cylinder is $2:5$.If its curved surface is $\frac{3960}{7}sq.cm$, find the height and radius. (use $\pi =\frac{22}{7}$)

Answer 1

Let $r$ and $h$ be the radius and height of the right circular cylinder respectively.

Given that $r:h=2:5$ $\Rightarrow \frac{r}{h}=\frac{2}{5}$. Thus $r=\frac{2}{5}h$

Now, the curved surface area $CSA=2\pi rh$

$\Rightarrow 2\times \frac{22}{7}\times \frac{2}{5}\times h\times h=\frac{3960}{7}$

$h^2=\frac{3960\times 7\times 5}{2\times 22\times 2\times 7}=225$

Thus, $h=15$ $\Rightarrow$ $r=\frac{2}{5}h=6$

Hence, the height of the cylinder is $15cm$ and the radius is $6cm$.