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# Differential equations watch

1. Can anyone show me how to solve this?
I am not really sure where to even begin.

Write a differential equation to express this:

(a) The rate at which the volume of a sphere changes with radius is proportional to the square of the radius.
2. Differentiate the formula for the volume of a sphere with respect to the radius and then see what you get
3. (Original post by wightsnowolf)
Differentiate the formula for the volume of a sphere with respect to the radius and then see what you get
I got 4pir^2, thanks.
4. That's right. So that shows that the rate of change of volume with respect to the radius is proportional to the radius squared, where the constant of proportionality is 4*pi

Since it will be proportional if V ' = k (r^2)

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