# Volumes of Revolution - Ellipsoid

1. Aug 28, 2009

### Noir

1. The problem statement, all variables and given/known data
An ellipse is rotated around the y-axis, find the volume of this solid.

2. Relevant equations
x^2 / a^2 + y^2 / b^2 = 1
$$\pi\int_{a}^-a x^2 dy$$

3. The attempt at a solution
I'm having trouble solving this; I know that the upper and lower bounds of the curve occur on the y-axis so I think that the ellipse equation can be rearranged to form;
x^2 / a^2 + 0 = 1
Thats where the upper and lower bounds for the integral come from.
However I know that the volume of an ellipsoid is V = 4/3*pi*a*b^2.
I just can't seem to get it to work.

Any help is appreciated :)

2. Aug 28, 2009

### rock.freak667

Shouldn't your limits be ±b ?

$$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \Rightarrow \frac{x^2}{a^2}=1-\frac{y^2}{b^2}$$

find x2 in terms of y2, then put that into π∫x2 dy from b to -b and calculate.