Volume Formulas Quick Card Cheat Sheet

Key Facts

• The volume of a rectangular prism is $V = lwh$, where $l$ is length, $w$ is width, and $h$ is height.
• The volume of any prism is $V = Bh$, where $B$ is the area of the base and $h$ is the perpendicular height.
• The volume of a cylinder is $V = \pi r^{2}h$, where $r$ is the radius and $h$ is the height.
• The volume of a pyramid is $V = \frac{1}{3}Bh$, where $B$ is the area of the base and $h$ is the perpendicular height.
• The volume of a cone is $V = \frac{1}{3}\pi r^{2}h$, where $r$ is the radius and $h$ is the perpendicular height.
• The volume of a sphere is $V = \frac{4}{3}\pi r^{3}$, where $r$ is the radius.
• For composite solids, split the figure into simpler solids and add or subtract their volumes using $V_{\text{total}} = V_{1} + V_{2}$ or $V_{\text{remaining}} = V_{1} - V_{2}$.
• Volume is measured in cubic units, such as $\text{cm}^{3}$, $\text{m}^{3}$, or $\text{in}^{3}$.

Vocabulary

Volume

Volume is the amount of three-dimensional space inside a solid.

Base Area

Base area is the area of the two-dimensional face used as the base of a prism, pyramid, cylinder, or cone.

Height

Height is the perpendicular distance from the base to the opposite face, vertex, or center level.

Radius

Radius is the distance from the center of a circle or sphere to its edge.

Composite Solid

A composite solid is a three-dimensional figure made from two or more simpler solids.

Cubic Unit

A cubic unit is a unit for measuring volume, representing a cube with side length $1$ unit.