Question

If the ratio between the curved surface area and the total surface area of a right circular cylinder is $3:4$, find the ratio of height to the radius of the cylinder.

Answer 1

$\frac{C.S.A}{T.S.A}=\frac{2\pi rh}{2\pi r(r+h)}=\frac{3}{4}$

$\Rightarrow \frac{h}{r+h}=\frac{3}{4}$

$\Rightarrow 4h=3r+3h$

$\Rightarrow h=3r$

$\Rightarrow \frac{h}{r}=3$