Integrated Math 3 / Unit 7: Geometric Modeling
7.1 Volume of Prisms and Cylinders
Notes
For any prism or cylinder, $V = Bh$ where $B$ is the area of the base and $h$ is the height.
- Rectangular prism: $V = lwh$.
- Cylinder: $V = \pi r^2 h$.
- Triangular prism: the base is a triangle, so $\displaystyle V = \left(\frac{1}{2}bh_{\text{tri}}\right) \cdot \text{length}$.
- Doubling the radius multiplies the volume by 4, since $r$ is squared.
Practice
What is the volume of a cylinder with radius 3 and height 10?
$V = \pi r^2 h = \pi(9)(10) = 90\pi$.
A triangular prism has a triangular base with base 6 and height 4, and a length of 10. What is its volume?
Base area $\displaystyle = \frac{1}{2}(6)(4) = 12$, and $V = 12 \cdot 10 = 120$.
The radius of a cylinder is doubled and its height stays the same. How does the volume change?
$V = \pi r^2 h$, and $(2r)^2 = 4r^2$.
Ready for more? Take the Unit 7 test.