Question

Question 119

The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2. Find the ratio between the height and radius of the cylinder.

Answer 1

Curved surface area of a cylinder $=2\pi rh$
Total surface area of a cylinder $=2\pi r(r+h)$
The ratio between the curved surface area and the total surface area of a cylinder is 1 : 2
$\therefore \frac{1}{2}=\frac{2\pi rh}{2\pi r(r+h)}\Rightarrow \frac{1}{2}=\frac{h}{(r+h)}\Rightarrow 2h=(r+h)\Rightarrow 2h-h=r\Rightarrow h=r$
$\therefore$ Ratio of height and radius = 1 : 1