# Solids of Revolution

• Dec 14th 2007, 06:18 AM
coolio
Solids of Revolution
Could use some help on this one:

To make a doughnut for breakfast, rotate about the y-axis the disk bounded by (x-7)^2 + y^2 = 9 , centered at (7,0). Write a definite integral that gives the volume of your breakfast. Evaluate the integral.

Thanks!
• Dec 14th 2007, 08:17 AM
galactus
By the Theorem of Pappus, To find the volume of a doughnut generated by revolving the disk of radius r about a line at a distance 'b' units from the center of the disk. The disk has radius 3 and is 7 units from the y-axis.

$V=2{\pi}\int_{-r}^{r}(b-x)(2\sqrt{r^{2}-x^{2}})dx$