Which expression gives the volume of a pyramid?

Which expression gives the volume of a pyramid?

• A. A=πr²
• B. A=2πrh+2πr²
• C. V=1/3Bh
• D. V=4/3πr³

Answer: (C)

Volume of a pyramid depends on how big the base is and how tall the shape is. The exact relationship is V = (1/3) × base area × height. Here, B is the area of the base and h is the perpendicular distance from the base to the apex. The one‑third factor comes from how the pyramid tapers as you move up from the base, which can be shown by slicing the pyramid into thin, similar layers. This makes the one‑third of the product B h the correct measure of the space inside. The other expressions correspond to different shapes: πr² is the area of a circle, 2πrh + 2πr² is the surface area of a cylinder, and (4/3)πr³ is the volume of a sphere.

Volume of a pyramid depends on how big the base is and how tall the shape is. The exact relationship is V = (1/3) × base area × height. Here, B is the area of the base and h is the perpendicular distance from the base to the apex. The one‑third factor comes from how the pyramid tapers as you move up from the base, which can be shown by slicing the pyramid into thin, similar layers. This makes the one‑third of the product B h the correct measure of the space inside. The other expressions correspond to different shapes: πr² is the area of a circle, 2πrh + 2πr² is the surface area of a cylinder, and (4/3)πr³ is the volume of a sphere.