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Math Help - related rates problem

  1. #1
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    related rates problem

    The volume of a sphere is increasing at a rate of 10 cm3/sec. Find the rate of change of its surface area when its volume is 32π/3 cm3.

    Using my crazy logic I ended up coming up with 20 / r... anything will help
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  2. #2
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    Quote Originally Posted by jawisbest View Post
    The volume of a sphere is increasing at a rate of 10 cm3/sec. Find the rate of change of its surface area when its volume is 32π/3 cm3.

    Using my crazy logic I ended up coming up with 20 / r... anything will help
    Find the radius r when the sphere has a volume of 32pi/3. Next, V = (4pi/3)*r^3, so V' = 4pi*r^2*r' = 10. Use this and the value you found for r to find r'. Also, A = 4pi*r^2, so A' = 8pi*r*r'. Use the values you found for r and r' to find A'.
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    So did all of that and came up with 4.367... can anyone confirm this?
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    Quote Originally Posted by jawisbest View Post
    So did all of that and came up with 4.367... can anyone confirm this?
    \frac{dS}{dt} \ne 4.367
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