Question

Mark the correct alternative of the following:
The total surface area of a cone of radius $$\dfrac{r}{2}$$ and length $$2l$$ is?

Answer 1

Correct option is B. $$\pi r\left(1+\dfrac{r}{4}\right)$$
Let $$r$$ and $$l$$ be the base radius and slant height of cone.

We know, the total surface area $$=\pi r (l+r)$$.

Here, it is given that,

the base radius is $$\dfrac{r}{2}$$ and that the slant height is $$2l.$$

Substituting these values in the above equation we have,

$$\implies$$ Total surface area $$=\pi\left(\dfrac{r}{2}\right)\left(2l+\dfrac{r}{2}\right)$$ $$=\pi r\left(l+\dfrac{r}{4}\right)$$.

Hence, option $$B$$ is correct.