Question

The ratio of the total surface area to the lateral surface area of the cylinder is $5:3$. Find the height of the cylinder, if the radius of the cylinder is $12cm$.

• A. $18cm$
• B. $16cm$
• C. $20cm$
• D. $14cm$

Answer 1

The correct option is A $18cm$

Let the height and radius of the cylinder be $h$ and $r$, respectively Then,
$\frac{\text{Total surface area}}{\text{Lateral surface area}}=\frac{2\pi rh+2\pi r^2}{2\pi rh}=\frac{2\pi r(r+h)}{2\pi rh}=\frac{r+h}{h}$

Given, $\frac{r+h}{h}=\frac{5}{3}$

$\Rightarrow \frac{12+h}{h}=\frac{5}{3}$

$\Rightarrow 36+3h=5h$

$\Rightarrow 2h=36$

$\Rightarrow h=18cm$