Geometry 12 5 Volume of Pyramids and Cones

Geometry 12. 5 Volume of Pyramids and Cones

Goals n n Find the volume of pyramids and cones. Solve problems using volume. 1/7/2022 Geometry 12. 5 Volume of Pyramids and Cones 2

Tempe City Hall 1/7/2022 Geometry 12. 5 Volume of Pyramids and Cones 3

Governor G. Hunt (1859 – 1934) 1/7/2022 Geometry 12. 5 Volume of Pyramids and Cones 4

Luxor Hotel, Las Vegas NV Pyramid Arena, Memphis TN 1/7/2022 Geometry 12. 5 Volume of Pyramids and Cones 5

Volume of a Pyramid Volume of the Prism V = Bh Volume of the Pyramid 1/7/2022 Geometry 12. 5 Volume of Pyramids and Cones 6

Volume of a Cone Volume of the Cylinder V = r 2 h Volume of the Cone 1/7/2022 Geometry 12. 5 Volume of Pyramids and Cones 7

Example 1 Find the volume. 6 8 8 1/7/2022 Geometry 12. 5 Volume of Pyramids and Cones 8

Example 2 Find the volume. 12 10 10 1/7/2022 Geometry 12. 5 Volume of Pyramids and Cones 9

Example 2 Solution ? h 12 5 10 10 1/7/2022 Geometry 12. 5 Volume of Pyramids and Cones 10

Example 2 Solution Solve for h: h 10. 91 12 5 10 10 1/7/2022 Geometry 12. 5 Volume of Pyramids and Cones 11

Example 2 Solution Solve for V: 12 10. 91 5 10 10 1/7/2022 Geometry 12. 5 Volume of Pyramids and Cones 12

Example 3 Find the volume of the pyramid with a regular hexagonal base. h = 15 6 1/7/2022 Geometry 12. 5 Volume of Pyramids and Cones 13

Example 3 Solution Area of the base: h = 15 6 3 6 1/7/2022 Geometry 12. 5 Volume of Pyramids and Cones 14

Example 3 Solution Area of the base: h = 15 6 1/7/2022 Geometry 12. 5 Volume of Pyramids and Cones 15

Example 4 Find the volume of the right circular cone. 12 5 1/7/2022 Geometry 12. 5 Volume of Pyramids and Cones 16

Example 5 Find the volume of the right circular cone. 15 6 1/7/2022 Geometry 12. 5 Volume of Pyramids and Cones 17

Example 5 Find h: Solution 15 h 6 1/7/2022 Geometry 12. 5 Volume of Pyramids and Cones 18

Example 5 Solution Find the volume: 15 13. 75 6 1/7/2022 Geometry 12. 5 Volume of Pyramids and Cones 19

Summary The volume of a pyramid is 1/3 the volume of a prism with the same measurements. n The volume of a cone is 1/3 the volume of a cylinder with the same measurements. n 1/7/2022 Geometry 12. 5 Volume of Pyramids and Cones 20

h h r Add these to your formula sheet. 1/7/2022 Geometry 12. 5 Volume of Pyramids and Cones 21

Find the volume of each figure. 20 19. 36 12 14 5 14 1/7/2022 Geometry 12. 5 Volume of Pyramids and Cones 22

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? 1/7/2022 Geometry 12. 5 Volume of Pyramids and Cones 23

Solution Cone Pyramid 1/7/2022 Geometry 12. 5 Volume of Pyramids and Cones 24