How do you:
Find the rate of change of the surface area of a cone when the radius is 2 meters and the volume is increasing at a rate of 6 pi meters/sec

Question

How do you:
Find the rate of change of the surface area of a cone when the radius is 2 meters and the volume is increasing at a rate of 6 pi meters/sec

anonymous · Answer

first you need to find the equation for the surface area of a cone

anonymous · Answer

SA = πr(r + l)

anonymous · Answer

then you need the volume formula

anonymous · Answer

$$V=\pi r ^{2}\frac{ h }{ 3 }$$

anonymous · Answer

using this and$$h ^{2}+r ^{2}=l ^{2}$$

anonymous · Answer

you can find the rate of change of h which will allow you to find the rate of change of l that you can then use to find the rate of change of the surface area

anonymous · Answer

remember it says that r is 2 meters so the radius is not changing so r can be treated as a constant when taking the derivative

anonymous · Answer

thank you very much!