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Rate of change question

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?
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?


dAdt=ddt(A)=2\displaystyle \frac{dA}{dt}=\frac{d}{dt}(A)=2

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 A=4πr2A=4\pi r^2 which you can use to get r, dAdr=8πr\frac{dA}{dr}=8\pi r , and drdt=drdA⋅dAdt\frac{dr}{dt}=\frac{dr}{dA} \cdot \frac{dA}{dt}

You can do this then.
(edited 7 years ago)
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razzor
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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?
(edited 7 years ago)

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