After studying various 3D shapes and finding formulas for their volumes, I challenged my students to invent a new shape. Lindsay created a shape with height that is circular at the top with radius but square at the bottom with side length Lindsay created this shape from a paraboloid: sliced four times parallel to the paraboloid's axis and two times perpendicular to the paraboloid's axis. Lindsay's shape is pictured below.
Find the volume of Lindsay's shape in which can be written as with integers, and coprime, and positive.
Give the value of