Question

A cone with a radius of 3 inches has a total area of 24 pi sq in. Find the volume of the cone.

Answer 1

Since you used the word "total" area, I assume the circular base is included.
Area of base = 9π
which leaves 15π for the area of the side of the cone.
The surface area without the base is
πrs, where s is the slant height
π(3)s = 15π
s = 5

so from our sketch of the cone we can see a right-angled triangle, with h as the height of the cone
h^2 + 3^2 = 5^2
h^2=16
h = 4

Volume of cone = (1/3)π(3^2)(4) = 12π cubic inches

Answer 2

15