Volume & Surface Area: Volume of Pyramid & Cone

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

Practice

📖 Learning Guide

Pyramid

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

Right Pyramid

A pyramid where the apex is vertically aligned directly above the geometric center of the base.

Oblique Pyramid

A pyramid where the apex is shifted and not vertically aligned above the base center. The perpendicular height drops to the plane containing the base outside its center.

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

What is volume?

Volume is the amount of three-dimensional space occupied by an object. It is measured in cubic units, such as cubic centimeters (cm³) or cubic meters (m³).

How do you calculate the volume of a box?

The volume of a box (rectangular prism) is calculated by multiplying its length, width, and height: V = l × w × h.

Volume of Pyramids & Cones — Practice & Guide | SealMath