Question

A sphere, a cylinder and a cone are of the same radius and same height. Find the ratio of their curved surface.

• A. $4:2:\sqrt{2}$
• B. $2:4:\sqrt{3}$
• C. $4:3:\sqrt{2}$
• D. $2:4:\sqrt{2}$

Answer 1

The correct option is A $4:2:\sqrt{2}$

Since the radius and the height are same, so let it be $r$ cm.

Thus, the height of the cylinder and the cone is $r$ cm.
Curved surface area of the sphere $=4\pi r^2$
Curved surface area of the cylinder $=2\pi rh=2\pi r\times r=2\pi r^2$
Curved surface area of the cone $=\pi rl=\pi r\times \sqrt{r^2+r^2}=\sqrt{2}\pi r^2$
$\therefore$ the ratio of their curved surfaces $=4\pi r^2:2\pi r^2:\sqrt{2}\pi r^2=4:2:\sqrt{2}$