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?
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,