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# Rate of change question

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1. 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?
2. (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?

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 which you can use to get r, , and

You can do this then.
3. (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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