Surface Area and Volume of 3D Shapes

Vocabulary flashcards covering the surface area and volume formulas, variables, and units for various 3D geometric shapes.

Surface Area (SA)

The total area of all the faces of a 3D shape, measured in square units (e.g., $\text{cm}^2$), representing how much is on the outside.

Volume (V)

The space occupied by a 3D shape, measured in cubic units (e.g., $\text{cm}^3$), representing how much is on the inside.

Cube - Surface Area

$\text{SA} = 6a^2$, where $a$ is the side length.

Cube - Volume

$V = a^3$, where $a$ is the side length.

Cuboid (Rectangular Prism) - Surface Area

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

Cuboid (Rectangular Prism) - Volume

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

Cylinder - Surface Area

$\text{SA} = 2\pi r(r + h)$, where $r$ is radius and $h$ is height.

Cylinder - Volume

$V = \pi r^2 h$, where $r$ is radius and $h$ is height.

Sphere - Surface Area

$\text{SA} = 4\pi r^2$, where $r$ is radius.

Sphere - Volume

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

Hemisphere - Surface Area

$\text{SA} = 3\pi r^2$ (curved surface area + base area), where $r$ is radius.

Cone - Surface Area

$\text{SA} = \pi r(l + r)$, where $r$ is radius and $l$ is slant height.

Cone - Volume

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

Square Pyramid - Surface Area

$\text{SA} = a^2 + 2al$, where $a$ is base side and $l$ is slant height.

Square Pyramid - Volume

$V = \frac{1}{3}a^2 h$, where $a$ is base side and $h$ is height.

Triangular Prism - Surface Area

$\text{SA}=2B+Ph$ , where b, is base, P is perimeter, and h, is height

Triangular Prism - Volume

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

Pi ($\pi$)

A mathematical constant commonly represented as $3.1416$ or $\frac{22}{7}$.