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27 December, 04:54

A sphere and a cone have the same volume. Each figure has a radius of 3 inches. What is the height of the cone

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  1. 27 December, 05:16
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    Sphere

    V = ⁴/₃πr³

    V = ⁴/₃ (3.14) (3) ³

    V = ⁴/₃ (3.14) (27)

    V = ⁴/₃ (84.78)

    V = 113.04in³

    Cone

    V = ¹/₃πr²h

    113.04 = ¹/₃ (3.14) (3) ² (h)

    113.04 = ¹/₃ (3.14) (9h)

    113.04 = ¹/₃ (28.26h)

    113.04 = 9.42h

    9.42 9.42

    12 = h

    The height of the cone is 12 inches.
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