Which solid uses the volume formula V = (1/3) × base area × height?

• A. Cone
• B. Sphere
• C. Cylinder
• D. Pyramid

Answer: (D)

For a pyramid, the volume is one-third of the product of its base area and its height. This comes from imagining the pyramid built from many slices parallel to the base: each slice is a smaller pyramid similar to the whole, and when you sum those slices from the base up to the apex, their total volume ends up being (1/3) × (base area) × height. This same form is used for cones if you treat the base as the circular base, giving V = (1/3) × base area × height (which is (1/3)πr^2h in that case). The cylinder uses base area × height without the 1/3, and a sphere has a different formula, 4/3 π r^3. Therefore, the solid described by V = (1/3) × base area × height is the pyramid.