Question

What is the total surface area of a cone of base radius $r$, height $h$, and slant height $l$?

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

Answer 1

The correct option is C $\pi rl+\pi r^2$


The curved surface area of a cone of base radius $r$, height $h$, and slant height $l$ is $\pi rl$.

Total surface area = curved surface area + base area

Here, base is a circle of radius $r$.
So, base area = $\pi r^2$
Therefore, total surface area of the cone = $\pi rl+\pi r^2$