# [SOLVED] Volume of a cylinder

• Mar 6th 2010, 09:32 AM
mybrohshi5
[SOLVED] Volume of a cylinder
I really dont know what im doing wrong. My online homework says this is wrong but im really sure its right :(

Can someone look this over for me. Thank you

The region bounded by http://webwork2.asu.edu/webwork2_fil...2c978940f1.png and http://webwork2.asu.edu/webwork2_fil...c777a8cb21.png is rotated about the line http://webwork2.asu.edu/webwork2_fil...2a969b3ca1.png.
Using cylindrical shells, set up an integral for the volume of the resulting solid.

Equation to use:

$\displaystyle V = \int^a_b 2\pi r h dx$

r = right - left
h = top - bottom

i sketched the graph and this is what i get from it

r = 11 - x
h = 8x - x^2 - x ---> 7x - x^2

so my final volume formula will be

$\displaystyle V = \int^7_0 2\pi (11-x)(7x-x^2) dx$

I evaluate that and get

$\displaystyle 2\pi(428.75)$

V = 2693.9157

Can anyone find anything wrong with this?

Thank you for any help :)

• Mar 6th 2010, 09:34 AM
mybrohshi5
Ok i just feel really stupid for writing up that whole post.

It asks for the integral that will be evaluated not to actually evalute it haha