Study Guide

Volume of Pyramids & Cones

Volume of Pyramids & Cones

The formula for the volume of pyramids and cones tells you how much space is inside each object.

For these two solid shapes, the volume formula is the same: it's one-third of the area of the base times the height.

Volume of Pyramids or Cones = ⅓ Area of Base × height = 1/3Bh

Area of base × height, or Bh? That looks familiar, but what's up with the 1/3? Picture this: a cone paper cup fits perfectly inside a cylinder cup. They're the same height and the round circles on top are also the same, which means the base of the cone and the base of the cylinder have the same area. How many paper cups of water does it take to fill the cylinder? Believe us when we say it takes 3, and a whole roll of paper towels to clean up the mess. The volume of three cones is equal to the volume of one cylinder with the same base and height. Similarly, the volume of three pyramids is real to the volume of one prism with the same base and height. 

cones and cylinder

The volume of each cone is equal to ⅓Bh = ⅓(28.3 × 10) = 94 ⅓ cm3. The volume of all three cones combined equals 283 cm3. The volume of the cylinder is equal to Bh = 28.3 × 10 = 283 cm3. Ta-da!

Pyramids and box

The volume of each pyramid is equal to ⅓Bh = ⅓(18 × 8) = 48 cm3. The volume of all three pyramids combined equals 144 cm3. The volume of the rectangular prism is equal to Bh = 18 × 8 = 144 cm3.