Question

The diameters of two cones are equal. If their slant heights are in the ratio 3:4, then find the ratio of their curved surface areas.

• A. 3 : 5
• B. 5 : 4
• C. 2 : 3
• D. 3 : 4

Answer 1

The correct option is D

3 : 4

Diameters of cones are equal i.e. $r_1=r_2=r$

Curved surface area of first cone
$=\pi \times r\times l_1$

Curved surface area of second cone
$=\pi \times r\times l_2$

Ratio of curved surface areas
$=\frac{CSAofcone1}{CSAofcone2}$

$=\frac{\pi \times r\times l_1}{\pi \times r\times l_2}=\frac{3}{4}=3:4$