Conic

[rinspd]

a/if an ellipse is rotated about its major axis, find the volume of the resulting solid?b/if an ellipse is rotated about its minor axis, find the resulting volume

 

[galactus]

Ellipse equation:

\(\displaystyle \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\)

For the major axis, solve the ellipse equation for y.

Then, use washers to revolve about the x axis from 0 to a.

Don't forget to multiply by 2.

For the minor axis, solve the ellipse equation for x in terms of y.

Then, revolve about the y axis using washers from 0 to b.

Don't forget to multiply by 2.