Surface Area & Volume Formulas Cheat Sheet

A printable reference covering surface area, volume, prisms, cylinders, pyramids, cones, spheres, and composite solids for grades 6-10.

Download PNG

Related Tools

Related Labs

Related Worksheets

Related Infographics

This cheat sheet covers the most important surface area and volume formulas for common three-dimensional shapes. Students need these formulas to solve problems involving packaging, containers, buildings, and real objects. It helps organize many similar formulas so they are easier to compare and remember. The goal is to connect each formula to the shape dimensions it uses. Surface area measures the total outside area of a solid, while volume measures the space inside it. Prisms and cylinders use the idea that volume equals base area times height, written as $V = Bh$ . Pyramids and cones have one third of the volume of a matching prism or cylinder, written as $V = \frac{1}{3}Bh$ . Spheres use formulas involving $\pi$ and the radius, including $V = \frac{4}{3}\pi r^{3}$ and $SA = 4\pi r^{2}$ .

Key Facts

The volume of any prism or cylinder is $V = Bh$ , where $B$ is the area of the base and $h$ is the height.
The volume of any pyramid or cone is $V = \frac{1}{3}Bh$ , where $B$ is the area of the base and $h$ is the perpendicular height.
The surface area of a rectangular prism is $SA = 2lw + 2lh + 2wh$ , where $l$ is length, $w$ is width, and $h$ is height.
The volume of a rectangular prism is $V = lwh$ , and the volume of a cube is $V = s^{3}$ .
The surface area of a cylinder is $SA = 2\pi r^{2} + 2\pi rh$ , and its volume is $V = \pi r^{2}h$ .
The surface area of a cone is $SA = \pi r^{2} + \pi r\ell$ , and its volume is $V = \frac{1}{3}\pi r^{2}h$ .
The surface area of a sphere is $SA = 4\pi r^{2}$ , and its volume is $V = \frac{4}{3}\pi r^{3}$ .
For composite solids, add volumes of joined parts, but do not include hidden interior faces when finding outside surface area.

Vocabulary

Surface Area: Surface area is the total area of all outside faces or curved surfaces of a three-dimensional figure.
Volume: Volume is the amount of space inside a three-dimensional figure, measured in cubic units.
Base Area: Base area is the area of the face or region used as the foundation in formulas such as $V = Bh$ .
Height: Height is the perpendicular distance from a base to the opposite face, vertex, or base plane.
Slant Height: Slant height is the diagonal height along the side of a cone or pyramid, often written as $\ell$ .
Radius: Radius is the distance from the center of a circle or sphere to its edge, often written as $r$ .

Common Mistakes to Avoid

Using slant height instead of vertical height for volume is wrong because volume formulas for cones and pyramids require the perpendicular height $h$ , not $\ell$ .
Forgetting the factor $\frac{1}{3}$ in cone and pyramid volume is wrong because these solids have one third the volume of a matching cylinder or prism.
Mixing up surface area and volume units is wrong because surface area is measured in square units such as $\text{cm}^{2}$ , while volume is measured in cubic units such as $\text{cm}^{3}$ .
Counting hidden faces in a composite solid is wrong because surface area includes only the outside surfaces that are visible or exposed.
Using diameter as radius is wrong because formulas such as $A = \pi r^{2}$ and $V = \pi r^{2}h$ require $r$ , and the radius is half the diameter.

Practice Questions

1 Find the volume of a rectangular prism with length $8\text{ cm}$ , width $5\text{ cm}$ , and height $3\text{ cm}$ .
2 Find the surface area of a cylinder with radius $4\text{ in}$ and height $10\text{ in}$ using $SA = 2\pi r^{2} + 2\pi rh$ .
3 Find the volume of a cone with radius $6\text{ m}$ and height $9\text{ m}$ using $V = \frac{1}{3}\pi r^{2}h$ .
4 Explain why a cone and a cylinder with the same base radius and height do not have the same volume.

Sign in to save