[SPLIT] The base of a solid is an ellipse in the xy-plane...

[Pre]

The base of a solid is an ellipse in the xy-plane with major axis of length 10 and minor axis at 6. Every cross section perpendicular to the major axis is a square. Find the volume of the solid.

Now unlike the other ones I really have no idea how to do this one. All what I know is that I think the equation for this ellipse is x^2/100 + y^2/36 = 1

 

[skeeter]

that is the correct equation for the ellipse

x²/100 + y²/36 = 1

vertical distance of the ellipse is the side of each square ... s = 2y

so, cross-sectional area is s² = 4y²

solving for y² ...

y²/36 = 1 - x²/100

y² = 36(1 - x²/100 )

\(\displaystyle \L V = \int_{-10}^{10} 144\left(1 - \frac{x^2}{100}\right) dx\)