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8 September, 07:59

A sphere with a radius of 3 cm has the same volume as a cone with a radius of 6 cm. What is the height of the cone?!

2 cm

3 cm

4 cm

5 cm

+4
Answers (1)
  1. 8 September, 08:22
    0
    Step-by-step explanation:

    VC = (1/3) ·pi·r2·h

    VC = volume of a cone

    r = radius of base of cone = 6 cm

    h = height

    VC = (1/3) ·pi·62·h

    VC = 12·pi·h

    VS = (4/3) ·pi·r3

    VS = volume of a sphere

    r = radius of base of sphere = 3 cm

    VS = (4/3) ·pi·33

    VS = 36·pi

    Since the volume of the cone and the sphere are equal:

    VC = VS

    12·pi·h = 36·pi

    Solve for h.
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