Can anyone help?Watch
and height 2r.
(i) Find the rate at which the volume is increasing when the radius is 2 cm and
increasing at a rate of 0.25 cm/s. 
(ii) Given that the volume is increasing at a rate of 5 cm
/s when the radius is 5 cm,
find the rate at which the surface area is increasing at this point. 
Can someone please talk me through this?
The volume of a cylinder is
where r is the radius and h the height.
We know that h=2r so
We want the rate at which the volume is increasing, i.e. dV/dt where t is the time.
It is given to us that when r=2, dr/dt=0.25cm/s, or more conveniently, 1/4 cm/s.
Using the chain rule on the formula for V above yields
Finding dV/dr is fairly easy, and we already have dr/dt - can you finish it off from here?
Can you tell me what you got for the first part? Just checking that you actually understand the hints. If you still haven't wrote it down I recommend doing that first before moving onto part II; I'm sure someone else will be willing to help on the off chance that I don't check back on TSR after this (going to eat now )
Write down a formula for surface area, A, in terms of r (don't forget the area of the base)
Then it is almost the same as the first part. You are given dV/dt and want dA/dt
Surface area of cylinder is
You are given so evaluate and then use
Can you complete it from here?
I just done this again and got 1/5Pi. No idea what I'm meant to be doing