Volume & Surface Area: Volume of Pyramid & Cone

Q: How do you calculate the volume of a pyramid?

The volume of a pyramid is calculated using: $V = \frac{1}{3} B h$, where $B$ is the base area and $h$ is the perpendicular height. For a square base, $B = s^2$.

Q: How do you calculate the volume of a cone?

The volume of a cone is calculated using: $V = \frac{1}{3} \pi r^2 h$, where $r$ is the radius of the circular base and $h$ is the height.

Learn how to calculate the volume of pyramids, cones, and composite 3D shapes. Interactive practice problems with step-by-step solutions.

Practice

📖 Learning Guide

Regardless of whether the pyramid is right or oblique, the volume is calculated using the following formula:

Volume of a Pyramid (Square)

V = \frac{1}{3} s^2 h

A pyramid is a three-dimensional solid with a polygonal base and triangular lateral faces that meet at a single point called the apex.

2. Volume of a Cone

A cone has a circular base of radius

r

and height

h

. Like a pyramid, its volume is exactly one-third of the cylinder that shares the same base and height. The base area is

B = \pi r^2

, so the volume is:

Cone

A cone is a three-dimensional solid with a circular base that tapers smoothly to a single point called the apex.

Volume of a Cone

V = \frac{1}{3} \pi r^2 h

3. General Formula

For any pyramid or cone, the volume is always one-third of the base area

B

multiplied by the height

h

Volume of a Pyramid or Cone (General)

V = \frac{1}{3} B h

Pyramids and cones have the same general volume formula: one-third of the base area times the height.

Learning Topics

Frequently Asked Questions

How do you calculate the volume of a pyramid?

The volume of a pyramid is calculated using:

V = \frac{1}{3} B h

, where

B

is the base area and

h

is the perpendicular height. For a square base,

B = s^2

How do you calculate the volume of a cone?

The volume of a cone is calculated using:

V = \frac{1}{3} \pi r^2 h

, where

r

is the radius of the circular base and

h

is the height.