# How do you find the volume of the solid with base region bounded by the curve #9x^2+4y^2=36# if cross sections perpendicular to the #x#-axis are isosceles right triangles with hypotenuse on the base?

##### 1 Answer

Sep 12, 2014

The volume of the solid can be found by

Let us look at some details.

If we rewrite

we realize that it is en ellipse that spans from

By solving for

Since the area

So, the volume of the solid can be found by

by symmetry about the y-axis,