Find the total surface area of a cone of slant height '2l' and radius 'r/2'.

Correct option is D

Given:

The slant height $$l_s = 2l$$ and radius $$r = \frac{r}{2}$$​

Formula Used :

​$$A = \pi r l + \pi r^2$$​​

Solution:

Substitute the values into the formula for total surface area:

​$$A = \pi \left( \frac{r}{2} \right) (2l) + \pi \left( \frac{r}{2} \right)^2$$​​

Simplifying the expression:

​$$A = \pi \left( \frac{r}{2} \right) (2l) + \pi \frac{r^2}{4}$$​​

​$$A = \pi r l + \frac{\pi r^2}{4}$$​​

Thus, the total surface area of the cone is $$( \pi r l + \frac{\pi r^2}{4})$$​​