Surface Area and Volume of Three-Dimensional Figures

Vocabulary flashcards covering fundamental definitions and geometric formulas for three-dimensional figures.

Surface Area (SA)

The total area of all the outside surfaces of a three-dimensional object.

Volume (V)

The amount of space inside a three-dimensional object.

Prism

A three-dimensional object that has two identical and parallel bases.

Surface Area of a Rectangular Prism

$SA = 2(lw + lh + wh)$, where $l$ is length, $w$ is width, and $h$ is height.

Volume of a Rectangular Prism

$V = lwh$, where $l$ is length, $w$ is width, and $h$ is height.

Surface Area of a Triangular Prism

$SA = bh + (a + b + c)l$, where $b$ is the base of the triangle base, $h$ is the height of the triangle base, $(a + b + c)$ is the sum of the three side lengths, and $l$ is the length of the prism.

Volume of a Triangular Prism

$V = \frac{1}{2}bhl$, where $b$ is the base of the triangle, $h$ is the height of the triangle, and $l$ is the length of the prism.

Pyramid

A three-dimensional figure that has one base and triangular sides meeting at one vertex.

Surface Area of a Pyramid

$SA = \text{Base Area} + \text{Lateral Area} = B + \frac{1}{2}Pl$, where $B$ is the area of the base, $P$ is the perimeter of the base, and $l$ is the slant height.

Volume of a Pyramid

$V = \frac{1}{3}Bh$, where $B$ is the area of the base and $h$ is the height of the pyramid.

Cylinder

A three-dimensional object that has two circular bases and one curved surface.

Surface Area of a Cylinder

$SA = 2\pi r^2 + 2\pi rh$, where $r$ is the radius of the circular base and $h$ is the height of the cylinder.

Volume of a Cylinder

$V = \pi r^2h$, where $r$ is the radius of the circular base and $h$ is the height of the cylinder.

Cone

A three-dimensional figure that has one circular base and one vertex.

Slant Height of a Cone

$l = \sqrt{r^2 + h^2}$, where $r$ is the radius of the base and $h$ is the height of the cone.

Surface Area of a Cone

$SA = \pi r(r + l) = \pi r(r + \sqrt{r^2 + h^2})$, where $r$ is the radius of the base and $l$ is the slant height.

Volume of a Cone

$V = \frac{1}{3}\pi r^2h$, where $r$ is the radius of the base and $h$ is the height of the cone.

Sphere

A three-dimensional figure that is perfectly round.

Surface Area of a Sphere

$SA = 4\pi r^2$, where $r$ is the radius of the sphere.

Volume of a Sphere

$V = \frac{4}{3}\pi r^3$, where $r$ is the radius of the sphere.