If a right circular cone has a circular base with a diameter of length 16 cm and a volume of 320𝜋 cm3, find its lateral area in square centimeters.

Question

If a right circular cone has a circular base with a diameter of length 16 cm and a volume of 320𝜋 cm³, find its lateral area in square centimeters.

I thought the answer was 15. But it's saying it is wrong.

Answer 1

Lateral Area = PI * R * l (slant height)

(using 3.14 for PI)

To find slant height we need to find height from volume equation:

Diameter is 16 cm, so radius is 8 cm

Cone volume = 1/3 PI R^2 H

320 = 1/3 PI 8^2 * H

960 = PI * 64 * H

15 = PI * H

H = 4.78

By Pythagorean Theorem:

slant height^2 = (8)^2 + (4.78)^2

slant height = 9.32

Lateral Area = PI * R * l (slant height)

Lateral Area = PI * 8 * 9.32

Lateral Area = 234.12