Question

The ratio of the radius and the height of a right cone is 5:9. Then the ratio of total surface area to curved surface of the cone is :

• A. 2:3
• B. 4:9
• C. 18:13
• D. 9:4

Answer 1

The correct option is C 18:13

Given, r : h = 5 : 12
Let r = $5x$ and h = $12x$

From the relation $l^2=h^2+r^2$

The Slant height,
$l=\sqrt{(5x{)}^2+(12x{)}^2}$

$\Rightarrow l=13x$

Hence, the required ratio

$=\frac{\pi r(r+l)}{\pi rl}$

$=\frac{\pi \times 5x(5x+13x)}{\pi \times 5x\times 13x}$

= 18:13