JAMB 1986 · UME · Q41

Find the total surface area of a solid cone of radius $2\sqrt3$ cm and slant height $4\sqrt3$ cm.

Worked solution (try it first)

A solid cone has a curved surface $\pi rl$ and a circular base $\pi r^2$ , so the total is $\pi r(r + l)$ .
Here $r + l = 2\sqrt3 + 4\sqrt3 = 6\sqrt3$ .
So the area is $\pi \times 2\sqrt3 \times 6\sqrt3 = 12 \times 3 \times \pi$
$= 36\pi$ cm², option D.