Question

A solid cylinder of height $9$ m has its curved surface area equal to one-third of the total surface area. What is the radius of the base?

• A. $9$ m
• B. $18$ m
• C. $27$ m
• D. $30$ m

Answer 1

Answer: (B)

$18$ m

Given, height $=9$ m

We need to find radius of the base of cylinder.

Also given, Curved surface area $=\frac{1}{3}\times$ total surface area.

Curved surface of the solid cylinder $=2\pi r.h$
Total surface area $=2\pi r^2+2\pi rh$
Therefore, $2\pi rh=\frac{1}{3}(2\pi r^2+2\pi rh)$
$\Rightarrow 6\pi rh=2\pi r^2+2\pi rh$
$\Rightarrow 4\pi rh=2\pi r^2$

$\Rightarrow r=2h=2\times 9=18$ m