Find the volume of the solid whose base is the circle x^2+y^2=64 and the cross sections perpendicular to the x-axis are triangles whose height and base are equal.

Because the height and base of each cross section are equal, the area for any given cross section is where the base of each section occurring along the line is the vertical distance between the upper and lower halves of the circle .

We can write



so that



and so the area of each cross section is



Over the circular base of the solid, we have , so the volume of the solid is given by the integral

n kg drug dm beckham