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    Hi,

    I couldnt do the following question :

    The volume of air inside a spherical football placed in the sun expands at a rate proportional to the surface area of the ball.

    The volume of the ball, with radius r , is  \frac {4}{3} \pi r^3 and the surface area is  4 \pi r^2 . Form a differential equation to model the rate of change in the radius of the ball.



    Attempt :
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     \frac {dr}{dt}  =  \frac {dr}{dV} X \frac {dV}{dt}

    I can find out what  \frac {dr}{dV} is but i am having problems in finding   \frac {dV}{dt} as :


      \frac {dV}{dt}    = k X A

      \frac {dV}{dt}    = k  (4 \pi r^2)     and i dont know how to find k!


    Thanks!

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    You don't need to find k, just multiply \dfrac{\text{d}r}{\text{d}V} by 4k \pi r^2. You're only forming the differential equation, rather than finding a particular solution.
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    (Original post by Glutamic Acid)
    You don't need to find k, just multiply \dfrac{\text{d}r}{\text{d}V} by 4k \pi r^2. You're only forming the differential equation, rather than finding a particular solution.

    That just gives u  k . Doesnt sound right coz k is a constant.
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    (Original post by wizz_kid)
    That just gives u  k . Doesnt sound right coz k is a constant.
    That seems reasonable enough.
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    (Original post by Glutamic Acid)
    That seems reasonable enough.
    Koool.

    Thanks!
 
 
 
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