Question

Find the surface area of the cone in terms of pi.

Answer 1

The bottom circle has surface area
\[ \pi r^2 = \pi 3^2 = 9\pi \]
The lateral surface has area
\[ \pi r*hypotenuse = \pi r*\sqrt{r^2+h^2} = \pi 3*\sqrt{3^2+4^2} = \pi 3*5 = 15\pi \]
Where the hypotenuse is the length from the top to the base along the side.
Add the areas to get the total surface area:
\[ Area = 9\pi+15\pi = 24\pi \]