Surface Area of Cylinders Cones and Spheres Worked Examples Cheat Sheet

Key Facts

• The total surface area of a cylinder is $SA=2\pi r^2+2\pi rh$, where $r$ is the radius and $h$ is the height.
• The lateral surface area of a cylinder is $LA=2\pi rh$, which does not include the two circular bases.
• The total surface area of a cone is $SA=\pi r^2+\pi r\ell$, where $\ell$ is the slant height.
• The lateral surface area of a cone is $LA=\pi r\ell$, which is the curved surface only.
• The surface area of a sphere is $SA=4\pi r^2$, and there are no bases to add.
• If a cone gives radius $r$ and vertical height $h$ instead of slant height, use $\ell=\sqrt{r^2+h^2}$ before finding surface area.
• If the diameter is given, first find the radius using $r=\frac{d}{2}$.
• Surface area is measured in square units, such as $cm^2$, $m^2$, or $in^2$.

Vocabulary

Surface area

Surface area is the total area covering the outside of a three-dimensional figure.

Lateral area

Lateral area is the area of the curved or side surface, not including any bases.

Radius

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

Diameter

The diameter is the distance across a circle or sphere through its center, and $d=2r$.

Slant height

The slant height $\ell$ of a cone is the distance from the vertex to the edge of the circular base along the side.

Base

A base is a flat face of a solid, such as the circular top or bottom of a cylinder or the circular bottom of a cone.