1. Insert Lesson Title Here Course 3 8-6 Volume of Pyramids and Cones A pyramid is a three-dimensional figure whose base is a polygon, and all of the other faces are triangles. It is named for the shape of its base. A cone has a circular base. The height of a pyramid or cone is measured from the highest point to the base along a perpendicular line.

2. Course 3 8-6 Volume of Pyramids and Cones VOLUME OF PYRAMIDS AND CONES (2 2 )

3. Course 3 8-6 Volume of Pyramids and Cones Additional Example 1B: Finding the Volume of Pyramids and Cones 1313 V = 9 10 V = 30  94.2 in 3 V = Bh 1313 B = (3 2 ) = 9 in 2 Use 3.14 for . Find the volume of the figure. Use 3.14 for .

4. Course 3 8-6 Volume of Pyramids and Cones 1313 V = 9 7 V = 21  65.9 m 3 V = Bh 1313 B = (3 2 ) = 9 m 2 Use 3.14 for . Check It Out: Example 1B 7 m 3 m Find the volume of the figure. Use 3.14 for .

5. Course 3 8-6 Volume of Pyramids and Cones Additional Example 2: Exploring the Effects of Changing Dimensions A cone has a radius of 3 ft. and a height of 4 ft. Explain whether tripling the height would have the same effect on the volume of the cone as tripling the radius. When the height of the cone is tripled, the volume is tripled. When the radius is tripled, the volume becomes 9 times the original volume.

6. Check It Out: Example 2 A cone has a radius of 2 m and a height of 5 m. Explain whether doubling the height would have the same effect on the volume of the cone as doubling the radius. Insert Lesson Title Here Course 3 8-6 Volume of Pyramids and Cones Double the Radius Double the Height Original Dimensions 1313 V = r 2 h 1313 1313 1313 = (2 2 )5  20.93 m 3 1313 V = r 2 (2h) = (2 2 )(25) = (2 2) 2 (5) V = (2r) 2 h  41.87 m 3  83.73 m 3 1313 When the height of a cone is doubled, the volume is doubled. When the radius is doubled, the volume is 4 times the original volume.

7. Lesson Quiz: Part 1 Find the volume of the figure to the nearest tenth. Use 3.14 for . 78.5 in 3 Insert Lesson Title Here Course 3 8-6 Volume of Pyramids and Cones 1. the cone

8. Lesson Quiz: Part 2 Find the volume of each figure to the nearest tenth. Use 3.14 for . Yes; the volume is one-third the product of the base area and the height. So if you triple the height, the product would be tripled. Insert Lesson Title Here Course 3 8-6 Volume of Pyramids and Cones 3. Explain whether tripling the height of a cone would triple the volume.

9. Cylinders and Cones Practice 1.) The volume of a cylinder is approximately 235.5 in. 3 and the height is 3 in. What is the radius of the cylinder? r = 5 in. Insert Lesson Title Here Course 3 8-6 Volume of Pyramids and Cones