Question

The lateral surface area (in ${cm}^2$) of a cone with height $3$ cm and radius $4$ cm is:

• A. $62\frac{6}{7}$
• B. $52\frac{6}{7}$
• C. $31\frac{3}{7}$
• D. $15\frac{5}{7}$

Answer 1

Answer: (A)

We know, lateral/curved surface area of a cone $=\pi rl$, where $r$ is the radius of the cone and $l$ is the slant height.

For a cone, $l=\sqrt{h^2+r^2}$, where $h$ is the height.

Hence, $l=\sqrt{3^2+4^2}$

$⟹$ $l=\sqrt{25}$

$⟹$ $l=5$ cm.

Hence, Curved surface area of the cone $=\frac{22}{7}\times 4\times 5=62\frac{6}{7}{cm}^2$.

Therefore, option $A$ is correct.