# volume of solid of the revolution

• Aug 7th 2010, 11:35 PM
pico24
volume of solid of the revolution
Can someone show me how to get the points of intersection for this problem [i know one of them is (1,1)]
Problem:
Determine the volume of the solid of the revolution obtained by rotating about the Y-axis the region bounded by y = 5th sqrt of (x) AND y = 2x^2-3x+2 that lies in the first quadrant??

Any help greatly appreciated
• Aug 8th 2010, 12:15 AM
Vlasev
By 5th sqrt of (x) do you mean $\displaystyle \sqrt[5]{x}$?

I set both functions equal to each other. I tried to solve it, but it becomes a 10th degree polynomial, which I then ran through Mathematica and it has no closed form solution i.e. you will have to find the second point of intersection numerically.
• Aug 8th 2010, 01:50 AM
HallsofIvy
Actually, that's not the problem! The problem is that the two graphs do NOT intersect! There is NO bounded region to rotate around the y-axis.
• Aug 8th 2010, 01:59 AM
Vlasev
Actually there is a region as show in the graph

http://img705.imageshack.us/img705/6574/graphqy.jpg
• Aug 8th 2010, 02:20 AM
pico24
How do I get the second point of intersection numerically??
thanks
• Aug 8th 2010, 02:47 AM
Vlasev
• Aug 8th 2010, 02:54 AM
pico24
thanks mate, perfect!!
• Aug 8th 2010, 08:01 AM
HallsofIvy
Quote:

Originally Posted by Vlasev
Actually there is a region as show in the graph

http://img705.imageshack.us/img705/6574/graphqy.jpg

You are right. Don't know how I missed that. Thanks for the correction.