Question

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

• A. 2:3
• B. 3:5
• C. 7:9
• D. 8:5

Answer 1

The correct option is D

8:5

Let the radius and height of the cone be $r$ and $h$ respectively

Given, $r:h=3:4$

Let $r=3x$ then $h=4x$

From the relation $l^2=h^2+r^2$
$l=\sqrt{(3x{)}^2+(4x{)}^2}$

$=\sqrt{9x^2+16x^2}$

$=\sqrt{25x^2}$
$\therefore l=5x$

Required ratio$=\frac{\text{Total surface area of the cone}}{\text{Curved surface area of the cone}}=\frac{\pi r(r+l)}{\pi rl}$
$=\frac{\pi \times 3x\times (3x+5x)}{\pi \times 3x\times 5x}$
$=8:5$