Geometry / Unit 11: Area, Surface Area and Volume
11.3 Surface Area of Prisms and Cylinders
Notes
Surface area is the total area of all faces. Lateral area leaves out the bases.
- Prism: $SA = Ph + 2B$, where $P$ is the base perimeter, $h$ the height and $B$ the base area.
- Rectangular prism: $SA = 2(lw + lh + wh)$.
- Cylinder: $SA = 2\pi r h + 2\pi r^2$. Lateral area is $2\pi r h$.
- Example: a cylinder with $r = 2$ and $h = 5$ has $SA = 20\pi + 8\pi = 28\pi$.
Practice
Find the surface area of a box 3 by 4 by 5.
$2(12 + 15 + 20) = 94$.
Find the surface area of a cylinder with radius 3 and height 10.
$2\pi(3)(10) + 2\pi(3)^2 = 60\pi + 18\pi = 78\pi$.
A can's label wraps around the side only. The can has radius 4 cm and height 7 cm. Find the label's area.
The label is the lateral area: $2\pi(4)(7) = 56\pi$.
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