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29 May, 09:22

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

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  1. 29 May, 09:35
    0
    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
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