A spherical snowball melts so that its radius decreases at a rate of 4 in/sec. At what rate is the volume of the snowball changing when the radius is 8 in?

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Jazlene Martin · Accepted Answer

The formula for volume of a sphere is       V    =          4      3              r      3        π  Differentiating with respect to       t  , time.                    d        V                    d        t              =    4          r      2              (                        d          r                          d          t                    )      The rate of change of the snowball is given by                     d        V                    d        t            .  We know                     d        r                    d        t              =    -    4  .  We want to find the rate of change when       r    =    8  . Thus,                    d        V                    d        t              =    4                  (        8        )            2              (      -      4      )                          d        V                    d        t              =    4          (      64      )              (      -      4      )                          d        V                    d        t              =    -    1024  Consequently, the snowball&#039;s volume is shrinking at a rate of       -    1024                                       in                3                    sec

A spherical snowball melts so that its radius decreases at a rate of 4 in/sec....

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