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# C4 - first order differentiation watch

1. 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 and the surface area is . Form a differential equation to model the rate of change in the radius of the ball.

Attempt :
Spoiler:
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I can find out what is but i am having problems in finding as :

and i dont know how to find k!

Thanks!

2. You don't need to find k, just multiply by . You're only forming the differential equation, rather than finding a particular solution.
3. (Original post by Glutamic Acid)
You don't need to find k, just multiply by . You're only forming the differential equation, rather than finding a particular solution.

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

Thanks!

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