Question

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

Given that,
r:h = 3:4
Let r = $3x$ and h = $4x$

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

The Slant height:
$l=\sqrt{(3x{)}^2+(4x{)}^2}$
$\Rightarrow l=5x$

We know that,
Total surface area of cone
$=\pi r(r+l)$
Curved surface area of cone
$=\pi rl$

Hence, the required ratio
$=\frac{Totalsurfaceareaofcone}{Curvedsurfacearea}$

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

$=\frac{\pi \times 3x(3x+5x)}{\pi \times 3x\times 5x}$

$=8:5$