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Math Help - Derivations

  1. #1
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    Derivations

    Air is being pumped into a spherical balloon so that its volume increases at a rate of 80cm^3/s . How fast is the surface area of the balloon increasing when its radius is 11cm ?

    ... i found the derivative of Surface Area to be 8*pi*r*(dv/dt)=(ds/dt)

    i keep getting 7040*pi as my answer.. but its not correct.

    please help mee!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by calculus shmalculus View Post
    Air is being pumped into a spherical balloon so that its volume increases at a rate of 80cm^3/s . How fast is the surface area of the balloon increasing when its radius is 11cm ?

    ... i found the derivative of Surface Area to be 8*pi*r*(dv/dt)=(ds/dt)

    i keep getting 7040*pi as my answer.. but its not correct.

    please help mee!
    of course that's not correct, that's the wrong equation.

    recall, the surface area is given by A = 4 \pi r^2 and the volume is given by V = \frac 43 \pi r^3
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  3. #3
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    i know the equations for both..
    what i am asking is if i need to derivate the surface area equation and if so ho would i go about doing that..
    i have been attempting his problem for a while now..


    ugh..
    please help..
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by calculus shmalculus View Post
    i know the equations for both..
    what i am asking is if i need to derivate the surface area equation and if so ho would i go about doing that..
    i have been attempting his problem for a while now..


    ugh..
    please help..
    if you differentiate A implicitly, you will end up with dr/dt as opposed to dV/dt as you wrote.

    use the volume equation to find dr/dt, when r = 11

    then, use that for dr/dt when you implicitly differentiate the Area equation
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