Question

If the curved surface area of a solid right circular cylinder of height $h$ and radius $r$ is one-third of its total surface area, then

• A. $h=\frac{1}{3}r$
• B. $h=\frac{1}{2}r$
• C. $h=r$
• D. $h=2r$

Answer 1

The correct option is B $h=\frac{1}{2}r$

We know, curved surface area of a cylinder of radius "$R$" and height "$h$" $=2\pi Rh$
Total surface area of a cylinder of radius "$r$" and height "$h$" $=2\pi r(r+h)$
Given, $2\pi Rh=\frac{1}{3}\times 2\pi r(r+h)$
$\therefore h=\frac{1}{3}\times (r+h)$
$\therefore \frac{2}{3}h=\frac{1}{3}r$
$\therefore h=\frac{1}{2}r$