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7 July, 14:06

If a snowball melts so that its surface area decreases at a rate of 7 cm2/min, find the rate at which the diameter decreases when the diameter is 10 cm.

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  1. 7 July, 14:57
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    D = 10 cm, r = 5 cm;

    A = 4 r² π = 4 · 5² · 3.14 = 314 cm²

    In one minute:

    A 1 = 314 - 7 = 307 cm²

    307 = 4 r 1² π

    r 1² = 307: 12.56

    r 1² = 24.44

    r 1 = 4.944

    d 1 = 2 · 4.944 = 9.888 cm

    10 - 9.888 = 0.112

    Answer:

    The rate at which the diameter decreases is 0.112 cm / min.
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