Question

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

• A. 1:1
• B. 1:2
• C. 2:1

Answer 1

The correct option is A 1:1

Let r be the radius
Let h be the height
$CSAofacylinder=2\pi rh$
$TSAofacylinder=2\pi rh+2\pi r^2$

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

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

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

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

$\therefore \frac{h}{r}=1:1$