Surface Area

Rectangular Prism (Box)

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

Or: $SA = 2(lw + lh + wh)$

Cube: $SA = 6s^2$

Cylinder

$SA = 2\pi r^2 + 2\pi rh$

• $2\pi r^2$ = two circular bases
• $2\pi rh$ = lateral (curved) surface

Lateral surface only: $LA = 2\pi rh$

Sphere

$SA = 4\pi r^2$

Memory aid: Same as $\frac{dV}{dr}$ where $V = \frac{4}{3}\pi r^3$

Cone

$SA = \pi r^2 + \pi r\ell$

where:

• $\pi r^2$ = circular base
• $\pi r\ell$ = lateral surface
• $\ell$ = slant height

To find slant height: $\ell = \sqrt{r^2 + h^2}$ (Pythagorean theorem)

Pyramid

$SA = B + \frac{1}{2}P\ell$

where:

• $B$ = area of base
• $P$ = perimeter of base
• $\ell$ = slant height

Strategy

1. Identify all faces/surfaces
2. Find area of each
3. Add them up