Geometry / Unit 11: Area, Surface Area and Volume
11.6 Volume of Pyramids, Cones and Spheres
Notes
A pyramid or cone holds exactly one third of the prism or cylinder with the same base and height.
- Pyramid: $\displaystyle V = \frac{1}{3}Bh$. Cone: $\displaystyle V = \frac{1}{3}\pi r^2 h$.
- Sphere: $\displaystyle V = \frac{4}{3}\pi r^3$ and $SA = 4\pi r^2$.
- A hemisphere is half a sphere.
- Use the height $h$, not the slant height, for volume.
- Example: a cone with $r = 3$ and $h = 4$ has $\displaystyle V = \frac{1}{3}\pi(9)(4) = 12\pi$.
Practice
A square pyramid has a base edge of 9 and a height of 10. Find its volume.
$\displaystyle \frac{1}{3}(81)(10) = 270$.
A cone has radius 3 and height 7. Find its volume.
$\displaystyle \frac{1}{3}\pi(9)(7) = 21\pi$.
Find the volume of a sphere with radius 6.
$\displaystyle \frac{4}{3}\pi(216) = 288\pi$.
Ready for more? Take the Unit 11 test.