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Basic Geometry

Basic Geometry

At a Glance - 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 Base × height

Why? Here it is in a nutshell. The volume of three pyramids is equal to the volume of one prism with the same base and height. Similarly, the volume of three cones is equal to the volume of one cylinder with the same circular base and height.

cones and cylinder

The volume of each cone is equal to ⅓Bh = ⅓(28.3 × 10) = 94 ⅓ cm3. 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. All three pyramids combined equals 144 cm3. The volume of the prism is equal to Bh = 18 × 8 = 144 cm3.

Example 1


The base we are dealing with in this pyramid is the triangular base on the bottom.

Example 2


The base of this cone is a circle with a radius of 5 cm.

Example 3

A cone whose base has a diameter of 4 inches and a height of 8 inches is 3/4 of the way full. How much empty space is left?

First we need to find the volume of the whole cone.

Exercise 1

Find the volume of this square pyramid:

square pyramid

Exercise 2

Find the volume of this cone:


Exercise 3

Find the volume of a square pyramid whose base has a perimeter of 20 inches and a height of 10 inches.

Exercise 4

Find the volume of a cone with a height of 10 in. and a circumference around the base of 18π cm.

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