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# C2 Differetiation

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1. Question 2 Page 150:

A closed cylinder has total surface area equal to 600π. Show that the volume, Vcm3 , of this cylinder is given by the formula V=300πr – πr3, where r cm is the radius of the cylinder. Find the maximum volume of such a cylinder.

Can someone help me with this - I am geting lost on the order in which to rearrange the equation for h...

A = 2 pi rh + 2 pi r^2

2 pi rh + 2 pi r^2 = 600 pi

2pi (rh +r^2) = 600 pi

rh +r^2 = 300 pi

Now I am not sure if im on the right track OR where to go from here so I can substitute into the formula for the volume of a cylinder to get V=300πr – πr3

I am getting really frustrated :-(

Any step by step instructions would be great!
2. (Original post by christinajane)
Question 2 Page 150:

A closed cylinder has total surface area equal to 600π. Show that the volume, Vcm3 , of this cylinder is given by the formula V=300πr – πr3, where r cm is the radius of the cylinder. Find the maximum volume of such a cylinder.

Can someone help me with this - I am geting lost on the order in which to rearrange the equation for h...

A = 2 pi rh + 2 pi r^2

2 pi rh + 2 pi r^2 = 600 pi

2pi (rh +r^2) = 600 pi

rh +r^2 = 300 pi

Now I am not sure if im on the right track OR where to go from here so I can substitute into the formula for the volume of a cylinder to get V=300πr – πr3

I am getting really frustrated :-(

Any step by step instructions would be great!
You know the formula for the volume is pi r^2 h.

But the formula you're looking for doesn't contain h.

So, rearrange the equation you've found to make h the subject and then substitute into the formula for the volume, eliminating h.
3. You're on the right track:

Surface area is given by .

Now we don't want , we only want things in terms of , so solve for : and substitute into the formula for the volume so that , as required.
4. Let me know if you need help with the second part, but I think you'll be able to manage that .
5. (Original post by IrrationalRoot)
Let me know if you need help with the second part, but I think you'll be able to manage that .

Ahhh yes ok! I was getting stuck on how to get rid of the r in the denominator...below, I kept thinking I had to x by r to get rid of the denominator... or thinking that the r cancencelled out the r^2 above it :-(

I always make silly mistakes like that - so basically the r in the denominator cancels out the r to the left of it??

Yeah I can do the second bit think you - I was just geting frustrated because I couldn't understand how to get past that I posted earlier :-(
6. (Original post by christinajane)
...
Yes
7. (Original post by IrrationalRoot)
Let me know if you need help with the second part, but I think you'll be able to manage that .
Thank you very much by the way
8. (Original post by christinajane)
Thank you very much by the way
No problem .

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