A cone has a volume of 100 cubic inches and base area of 25 square inches. Malik is making a square prism that has three times the volume of the cone. The base of the prism has twice the area of the base of the cone. Select all that apply.

A The height of the cone is 12 inches

B The radius of the base of the cone is 5/π (pi) inches

C The side length of the base of the prism is 10 inches

D The height of the cone is twice the height of the prism

E The height of the cone is equal to the height of the prism

F The diameter of the base of the cone equals the side length of the base of the prism

Question

Mathematics

Lorelai Horn

24 May, 06:13

A cone has a volume of 100 cubic inches and base area of 25 square inches. Malik is making a square prism that has three times the volume of the cone. The base of the prism has twice the area of the base of the cone. Select all that apply.

A The height of the cone is 12 inches

B The radius of the base of the cone is 5/π (pi) inches

C The side length of the base of the prism is 10 inches

D The height of the cone is twice the height of the prism

E The height of the cone is equal to the height of the prism

F The diameter of the base of the cone equals the side length of the base of the prism

+5

Answers (1)

Know the Answer?

Braeden Atkinson · Answer 1

Answer: F The diameter of the base of the cone equals the side length of the base of the prism

Step-by-step explanation:

Given that the

volume = 100 cubic inches and base area = 25 square inches

The base area of a cone is the area of a circle

Area = π r^2

25 = 3.143 r^2

r ^2 = 25/3.143

r = sqrt (7.954)

r = 2.8

Volume = area * height

Height = volume/area

Height = 100/25 = 4 inches

Given that the prism has three times the volume of the cone.

Prism volume = 3 * 100 = 300

Cube root of 300 = 6.69 inches