Question

The radius and height of a right circular cone are in the ratio 3:4. Then the ratio of total surface area of the cone to its curved surface area is

• A. $2:3$
• B. $3:5$
• C. $7:9$
• D. $8:5$

Answer 1

The correct option is D

$8:5$

Let 'r' be the radius of the cone and 'h' be its height.
Given, r : h = 3 : 4.
Let $r=3x$ and $h=4x$.
We know, slant height is given by,
$l=\sqrt{h^2+r^2}$
$⟹l=\sqrt{(3x{)}^2+(4x{)}^2}$
$⟹l=5x$

Required ratio $=\frac{\text{TSA}}{\text{CSA}}=\frac{\pi r(r+l)}{\pi rl}=\frac{(r+l)}{l}=\frac{(3x+5x)}{5x}=\frac{8x}{5x}$

$\therefore \text{Required ratio}=8:5$