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    The surface area of a sphere is increasing at a rate of 2cm²/s.
    Find the rate of increase of the radius when the surface area is 100πcm².

    I know that dA/dt=2
    and I need to find dr/dA when A = 100


    by the chain rule, then supposedly it should be dr/dA = dr/dt x dA/dt
    so dr/dA = dr/dt x 2?

    Is that correct up to that point, and if so, how would I go about finding dr/dt?
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    (Original post by JaredzzC)
    The surface area of a sphere is increasing at a rate of 2cm²/s.
    Find the rate of increase of the radius when the surface area is 100πcm².

    I know that dA/dt=2
    and I need to find dr/dA when A = 100


    by the chain rule, then supposedly it should be dr/dA = dr/dt x dA/dt
    so dr/dA = dr/dt x 2?

    Is that correct up to that point, and if so, how would I go about finding dr/dt?
    \displaystyle \frac{dA}{dt}=\frac{d}{dt}(A)=2

    Not chain rule needed, just integrate both sides with respect to t.

    Edit: scrap that, there's a constant of integration in there to deal with.

    Just know that A=4\pi r^2 which you can use to get r, \frac{dA}{dr}=8\pi r , and \frac{dr}{dt}=\frac{dr}{dA} \cdot \frac{dA}{dt}

    You can do this then.
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    (Original post by JaredzzC)
    The surface area of a sphere is increasing at a rate of 2cm²/s.
    Find the rate of increase of the radius when the surface area is 100πcm².

    I know that dA/dt=2
    and I need to find dr/dA when A = 100


    by the chain rule, then supposedly it should be dr/dA = dr/dt x dA/dt
    so dr/dA = dr/dt x 2?

    Is that correct up to that point, and if so, how would I go about finding dr/dt?
    You should know that the surface area of a sphere is given by the formula A = 4*π *r²

    You know that A = 100π, so use this to find what r is.

    Also, by the chain rule, dr/dt = dr/dA * dA/dt

    Can you use this to find what dr/dt is?
 
 
 
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