Question

The total surface area of a cone whose radius is $2r$ and slant height $\frac{l}{2}$ is:

• A. $2\pi r(l+r)$
• B. $2\pi r(\frac{l}{2}+r)$
• C. $2\pi r(l+4r)$
• D. $\pi r(l+4r)$

Answer 1

The correct option is D $\pi r(l+4r)$

We know, the total surface area of a cone $=\pi R^2+\pi LR$, where $R$ is the radius and $L$ is the slant height.

Given, $R=2r$ and $L=\frac{l}{2}$.

Therefore, the total surface area of the cone $=\pi (2r{)}^2+\pi (\frac{l}{2}\left)\right(2r)=\pi 4r^2+\pi rl$ $=\pi r(l+4r)$.

Hence, the answer is $\pi r(l+4r)$.

Therefore, option $D$ is correct.