Geometry / Unit 11: Area, Surface Area and Volume
11.5 Volume of Prisms and Cylinders
Notes
Volume is the space inside a solid, in cubic units.
- Prism or cylinder: $V = Bh$ (base area times height).
- Cylinder: $V = \pi r^2 h$.
- Cavalieri's Principle: if two solids have the same height and equal cross-section areas at every level, they have the same volume. So an oblique (slanted) prism or cylinder uses the same formula.
- Example: a cylinder with $r = 2$ and $h = 5$ has $V = 20\pi$.
Practice
Find the volume of a cylinder with radius 3 and height 8.
$\pi(3)^2(8) = 72\pi$.
A triangular prism has a triangular base with base 6 and height 4. The prism is 10 long. Find its volume.
$\displaystyle B = \frac{1}{2}(6)(4) = 12$, so $V = 12 \cdot 10 = 120$.
A straight stack of 20 coins and a slanted stack of the same 20 coins have the same height. How do their volumes compare?
By Cavalieri's Principle, equal heights and equal cross sections give equal volumes.
Ready for more? Take the Unit 11 test.