The base of a certain solid is the triangle with vertices at (−6,3), (3,3), and the origin. Cross-sections perpendicular to the y-axis are squares. Then the volume of the solid?

Answer 1

Think of the solid as a stack of thin squares. At a distance y from the origin, the square has side 3y. So, add them all up and the volume is

∫[0,3] (3y)^2 dy