The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the diameter is 60 mm?

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Mylee Mcintyre · Accepted Answer

Let r be the radius or sphere and v be the volume at the sphere.we have volume or sphere   v  =      4    3    π      r    3  Given             d      r              d      t        =  4     m  m      /    sDifferentiate with t      d          d      t        (  v  )  =      d          d      t        [      4    3    π      r    3    ]    ⇒            d      v              d      t        =      4    3    π  ⋅      d          d      t        (      r    3    )    ⇒            d      v              d      t        =            4      π        3    (  3      r    2    )  ⋅            d      r              d      t          ⇒            d      v              d      t        =  4  π      r    2              d      r              d      t       (2)  At   D  =  60     m  m  ⇒  r  =      π    2    =      60    2    =  30     m  m    ⇒  (  2  )  ⇒            d      v              d      t        =  4  π  (  30      )    2    (  4  )  =  14400  π

The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the diameter is 60 mm?

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