Question

The ratio of the curved surface area to the total surface area of a right circular cylinder is 1 : 2. The ratio of the height to the radius of the cylinder is _____.

• A. 1 : 1
• B. 1 : 2
• C. 2 : 1
• D. 1 : 4

Answer 1

The correct option is A 1 : 1

Let $r$ and $h$ be the radius and the height of the cylinder respectively.
$CSAofthecylinder=2\pi rh$
$TSAofthecylinder=2\pi rh+2\pi r^2$

Given: $\frac{CSA}{TSA}=\frac{1}{2}$

$\Rightarrow \frac{2\pi rh}{2\pi rh+2\pi r^2}=\frac{1}{2}$

$\Rightarrow \frac{2\pi rh}{2\pi r\times (h+r)}=\frac{1}{2}$

$\Rightarrow \frac{h}{h+r}=\frac{1}{2}$
$\Rightarrow 2h=h+r$
$\Rightarrow h=r$

$\therefore h:r=1:1$