# Can anyone help?

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#1
A potter is making an open topped vessel shaped as a right circular cylinder of radius r
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. [5]
(ii) Given that the volume is increasing at a rate of 5 cm
3
/s when the radius is 5 cm,
find the rate at which the surface area is increasing at this point. [6]

Can someone please talk me through this?
0
#2
(Original post by arkanm)
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?
I get that. What about the second part?
1
#3
(Original post by arkanm)
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 )
6Pi
0
6 years ago
#4
(Original post by Fishfingers52)
I get that. What about the second part?
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
1
#5
(Original post by brianeverit)
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
Can you talk me through it please? I need to see what's happening
0
6 years ago
#6
(Original post by Fishfingers52)
Can you talk me through it please? I need to see what's happening
Surface area of cylinder is
Now find
You are given so evaluate and then use

Can you complete it from here?
0
#7
(Original post by brianeverit)
Surface area of cylinder is
Now find
You are given so evaluate and then use

Can you complete it from here?
From what you said I got 40, which I'm guessing is wrong :L
I just done this again and got 1/5Pi. No idea what I'm meant to be doing
0
6 years ago
#8
(Original post by Fishfingers52)
From what you said I got 40, which I'm guessing is wrong :L
I just done this again and got 1/5Pi. No idea what I'm meant to be doing

so
1
#9
(Original post by brianeverit)

so
I think I follow that one a lot better. Thanks
0
2 years ago
#10
Doesn't dv /dt = 5pi so the last calculation would be 50pi X 1/150pi X 5pi which equals 5/3pi? I'm not sure if I'm correct but I have this question for homework so it would be much appreciated if someone replied asap
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