# Proving a volume of a cylinder

1. May 22, 2006

### rachael

1. Show that a volume of a clyinder equals to v= A^2 \ (4πh)
where h= height of the cylinder
A = area of a original paper

how would i prove this question?
thank you

v= πr^2 h -------1
v=A^2 \ (4πh)-----2

i tried to make h da subject but i got 4v^2 = Ar^2 which it does work out

2. May 22, 2006

### arunbg

What is the curved surface area of a cylinder ?
Is it the area of paper used ?

3. May 22, 2006

### rachael

yes the area of the paper is used

4. May 22, 2006

### daveb

Since this is in the precalculus forum, i won't refer to integrals. The regular expression for the volume of a cylinder is nr^2h. The area of the paper is A. Find an expression for A in terms of n, r and h, and simply square that and divide by 4nh to show that this equals the volume of the sylinder.

5. May 22, 2006

### Hootenanny

Staff Emeritus
Just for the record, I prefer the integral form, much nicer and easier to understant I find.

~H

6. May 23, 2006

### rachael

thank you for your help though

7. May 23, 2006

### aujing

what is the meaning of "putting the 2 functions in the parathesis seperated by the colon" ??

8. May 23, 2006

### aujing

what's the meaning of
"A = area of a original paper"

yOU skipped the most important part !?
by folding a paper to form a cylinder !? I assume..
A=2πrh
V=πrrh = 2πrh2πrh\4πh = AA\4πh

@.u