The volume of a solid with cross sections, perpendicular to the -axis, of known area on isadditionally,
An ellipse with equation x^2 + 9y^2= 9 is the base of a solid in which each cross section perpendicular to the x axis is a square. find the volume of the solid.
i drew the graph of the ellipse and now i'm stuck
If we solve for in your equation, we get So, the area of the cross section at is
(squaring because the cross section is a square).
The total volume is then
I use and for the limits because the major axis of the ellipse is of length and it is centered at the origin.