Question

The curved surface area of a cone of slant height $l$ and radius $r$ is given by

• A. $\frac{1}{3}\pi r^2$
• B. $\pi rl$
• C. $\pi r{l}^2$
• D. $\frac{1}{3}\pi rl$

Answer 1

The correct option is B

$\pi rl$

Determine the curved surface area of a cone :

Explanation for correct option:

Option (B) : $\pi rl$

A cone is created by folding a sector of a circle with radius $l$, that forms the slant height of the cone.

So, the curved surface area of the cone is the product of the ratio of the circular length of the sector and the circumference of the circle with the area of the circle folded.

Determine the curved surface area:

$$\begin{gathered} CSA=\frac{2\mathrm{\pi r}}{2\mathrm{\pi l}}\times \pi l^2 \\ \Rightarrow CSA=\pi rl \end{gathered}$$

So, option (B) is correct.

Explanation for incorrect options:

Since the curved surface are is $\pi rl$.

So, options (A), (C), and (D) are incorrect.

Hence, option (B) is correct.