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Math Help - Rates of change

  1. #1
    Member helloying's Avatar
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    Rates of change

    Gas escapes from a spherical balloon at rate of 720cm^3 per second. Find the rate of change of the curface area when the radius is 36cm.

    Help me please . thank you very very much
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  2. #2
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    Quote Originally Posted by helloying View Post
    Gas escapes from a spherical balloon at rate of 720cm^3 per second. Find the rate of change of the curface area when the radius is 36cm.
    What is the formula for the volume V of a sphere having a radius of r?

    What is the formula for the surface area SA of a sphere having radius r?

    When r = 36, what is the surface area?

    Note that you are given that dV/dt = -720.

    Differentiate the "volume" formula with respect to time "t".

    Plug in the known values for dV/dt and r. Solve for dr/dt.

    If you get stuck, please reply showing how far you have gotten, starting with the "volume" and "surface area" formulas. Thank you!
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  3. #3
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    Quote Originally Posted by helloying View Post
    Gas escapes from a spherical balloon at rate of 720cm^3 per second. Find the rate of change of the curface area when the radius is 36cm.

    Help me please . thank you very very much
    You need to know the volume V and the surface area A of the sphere with radius r. Then differentiate both sides with respect to t.
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