Question

The diameters of two cones are equal. If their slant heights are in the ratio $5:3$, then find the ratio of their curved surface areas.

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

Answer 1

The correct option is D $5:3$

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
$=\frac{CSAofcone1}{CSAofcone2}$

$=\frac{\pi \times r\times l_1}{\pi \times r\times l_2}=\frac{5}{3}=5:3$