1. Find the Volume:
V = r2h = (242)(8) = 4608 in3
8 in
4 ft

2. Volume of Pyramids and Cones
Geometry
Mrs. Nakagawa

3. Objective
To learn and use the formulas for finding the volumes of pyramids and cones.

4. Reminder: What is a Pyramid?
Definition:
A shape formed by connecting triangles to a polygon.
Examples:

5. Reminder: What is a Cone?
Definition:
A shape formed from a circle and a vertex point.
Examples: s

6. Volume Of A Cone. Consider the cylinder and cone shown below: D
The diameter (D) of the top of the cone and the cylinder are equal. H
The height (H) of the cone and the cylinder are equal.
If you filled the cone with water and emptied it into the cylinder, how many times would you have to fill the cone to completely fill the cylinder to the top ?
3 times.
This shows that the cylinder has three times the volume of a cone with the same height and radius.

7. Formulas
Volume of a Cylinder:
V = r2 h
Volume of a Cone:
V= 1/3 pr2h

8. Example #1 Calculate the volume of: V= 1/3 pr2h V= 1/3 (p)(7)2(9)
V = 147pm3

9. Example #2 Calculate the volume of: V= 1/3 pr2h V= 1/3 (p)(5)2(12)
V = 100pcm3

10. Compare Compare a Prism to a Pyramid.
Make a conjecture to what the formula might be for Volume of a Pyramid.

11. Formulas
Volume of a Prism:
Volume of a Pyramid:
V = 1/3 Bh

12. Example #3 Calculate the volume of: V = 1/3 Bh V = 1/3 (102)(15)
15”
V = 1/3 Bh
V = 1/3 (102)(15)
V = 500in3
10”

13. Volumes of Pyramids and Cones
Homework
Quizstar:
Volumes of Pyramids and Cones