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27 October, 16:47

The volume of a sphere increases with the cube of its radius. If the radius of a sphere increases from 2 cm to 6 cm. by what factor does its volume increase

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  1. 27 October, 19:31
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    If im not wrong

    Answer

    volume increases with a factor of 27

    Explanation;

    The volume of a sphere is given by the formula

    V = 4/3 πr³

    When the radius is 2 cm the volume will be;

    V = 4/3 π (2) ³

    = 32/3 π

    When the increases to 6 cm the volume will be;

    V = 4/3 π (6) ³

    = 864/3 π

    Hence, the volume increases by a factor;

    (864/3 π) : (32/3 π)

    = 27

    Thus, the volume increases with a factor 27
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