Question

The curved surface area of a cylinder is three-fifth of its total surface area. Find the ratio between the height and the radius of the cylinder ?

• A. 3:2
• B. 2:5
• C. 3:5
• D. 8:3

Answer 1

Answer:

A. 3:2

For a cylinder:

Curved Surface Area (CSA) $= (2\pi rh)$
Total Surface Area (TSA) $= (2\pi r(h + r))$

Given:
$\text{CSA} = \frac{3}{5} \times \text{TSA}$

$2\pi rh = \frac{3}{5} \times 2\pi r(h + r)$

$Cancel (2\pi r):$
$h = \frac{3}{5}(h + r)$
5h = 3(h + r)
5h = 3h + 3r
$\Rightarrow 2h = 3r$
$\frac{h}{r} = \frac{3}{2}$

Ratio (height : radius) = 3 : 2