1. Geometry Volume of Pyramids and Cones

2. August 21, 2015 Goals Find the volume of pyramids and cones. Solve problems using volume. Skip Intro

3. August 21, 2015 Pyramids

4. August 21, 2015 Pyramid Polyhedron with a polygon base. Lateral faces are triangles. Lateral faces meet at a common vertex. Regular pyramid: base is a regular polygon. (This is what we will discuss.)

5. August 21, 2015 Square Pyramid Vertex Altitude (h) Slant Height ( l )

6. August 21, 2015 Tempe City Hall

7. August 21, 2015 Governor G. Hunt (1859 – 1934)

8. August 21, 2015 Luxor Hotel, Las Vegas NV Pyramid Arena, Memphis TN

9. August 21, 2015 Volume of a Pyramid Volume of the Prism V = Bh Volume of the Pyramid

10. August 21, 2015 Volume of a Cone Volume of the Cylinder V =  r 2 h Volume of the Cone

11. August 21, 2015 Example 1Find the volume. 8 6 8

12. August 21, 2015 Example 2Find the volume. 10 12

13. August 21, 2015 Example 2Solution 10 12 ? 5 h

14. August 21, 2015 Example 2Solution 10 12 5 Solve for h: 10.91 h

15. August 21, 2015 Example 2Solution 10 12 5 Solve for V: 10.91

16. August 21, 2015 Example 3 Find the volume of the pyramid with a regular hexagonal base. h = 15 6

17. August 21, 2015 Example 3 Solution h = 15 6 Area of the base: 6 3

18. August 21, 2015 Example 3 Solution h = 15 6 Area of the base:

19. August 21, 2015 Example 4 Find the volume of the right circular cone. 5 12

20. August 21, 2015 Example 5 Find the volume of the right circular cone. 6 15

21. August 21, 2015 Example 5 Solution 6 15 h Find h:

22. August 21, 2015 Example 5 Solution 6 15 13.75 Find the volume:

23. August 21, 2015 Summary The volume of a pyramid is 1/3 the volume of a prism with the same measurements. The volume of a cone is 1/3 the volume of a cylinder with the same measurements.

24. August 21, 2015 h r h Add these to your formula sheet.

25. August 21, 2015 Find the volume of each figure. 5 20 12 14 19.36

26. August 21, 2015 Final Problem The base of a square pyramid measures 12 ft on each side, and the height of the pyramid is 15 ft. A cone has a diameter of 12 ft and has the same volume as the square pyramid. What is the height of the cone?

27. August 21, 2015 Solution Pyramid Cone

28. August 21, 2015 Practice Problems