Question

A cone is inscribed in a cylinder. A square pyramid is inscribed in a rectangular prism. The cone and the pyramid have the same volume. Part of the volume of the cylinder, V1, is not taken up by the cone. Part of the volume of the rectangular prism, V2, is not taken up by the square pyramid. What is the relationship of these two volumes, V1 and V2?

Answer 1

V1 and V2 are equal

Explanation:

Answer 2

The volume of both a cone and a cylinder can be described by (area of the base) * (height of the solid) * (1/3), which we'll write as V = Bh/3. If we compare this formula to the volume formulas for cylinders and prisms, we see that if we multiply the volume of a cone by 3, we get the volume of the cylinder it is inscribed in. The same applies for a pyramid and the rectangular prism it is inscribed in. Both the cone and pyramid have the same volume V, so the cylinder and rectangular prism will have the same volume. Therefore, V1 and V2 are equal.