Integrated Math 3 / Unit 7: Geometric Modeling
7.3 Surface Area
Notes
Surface area is the total area of all faces.
- Prism: $SA = 2B + Ph$ (two bases plus the lateral rectangles). For a rectangular prism, $SA = 2(lw + lh + wh)$.
- Cylinder: $SA = 2\pi r^2 + 2\pi r h$.
- Sphere: $SA = 4\pi r^2$.
- Cone: $SA = \pi r^2 + \pi r \ell$, where $\ell$ is the slant height. Find $\ell$ with $\ell^2 = r^2 + h^2$.
Practice
What is the surface area of a rectangular prism that is 2 by 3 by 5?
$2(6 + 10 + 15) = 62$.
What is the surface area of a sphere with radius 5?
$4\pi r^2 = 4\pi(25) = 100\pi$.
A cone has radius 3 and height 4. What is its total surface area?
The slant height is $\displaystyle \sqrt{9 + 16} = 5$. $SA = \pi(9) + \pi(3)(5) = 24\pi$.
Ready for more? Take the Unit 7 test.