Surface Area and Volume

Nets

A net is a 2D pattern that folds into a 3D shape.

A rectangular prism's net has 6 rectangles (3 pairs of identical faces).

Surface Area

Surface area = total area of all faces of a 3D shape.

Rectangular Prism

$SA = 2lw + 2lh + 2wh$

Example: $l = 5$, $w = 3$, $h = 4$ $SA = 2(5)(3) + 2(5)(4) + 2(3)(4)$ $= 30 + 40 + 24 = 94 \text{ sq units}$

Cube

$SA = 6s^2$

Volume

Volume = amount of space inside a 3D shape (measured in cubic units).

Rectangular Prism

$V = l \times w \times h$

Example: $l = 5$, $w = 3$, $h = 4$ $V = 5 \times 3 \times 4 = 60 \text{ cubic units}$

Cube

$V = s^3$

With Fractional Edges

$V = 2\frac{1}{2} \times 3 \times 1\frac{1}{2} = \frac{5}{2} \times 3 \times \frac{3}{2} = \frac{45}{4} = 11\frac{1}{4}$

Units

• Surface area: square units ($\text{cm}^2$, $\text{in}^2$)
• Volume: cubic units ($\text{cm}^3$, $\text{in}^3$, $\text{ft}^3$)

Remember: Surface area tells you how much wrapping paper you need. Volume tells you how much stuff fits inside.