1. Our learning goal is to be able to solve for perimeter, area and volume. Learning Goal Assignments 1.Perimeter and Area of Rectangles and Parallelograms 2.Perimeter and Area of Triangles and Trapezoids 3.The Pythagorean Theorem 4.Circles 5.Drawing Three-Dimensional figures 6.Volume of Prisms and Cylinders 7.Volume of Pyramids and Cones 8.Surface Area of Prisms and Cylinders 9.Surface Area of Pyramids and Cones 10.Spheres

2. Pre-Algebra 6-7 Volume of Pyramids and Cones Learning Goal Assignment Learn to find the volume of pyramids and cones.

3. Pre-Algebra 6-7 Volume of Pyramids and Cones Pre-Algebra HOMEWORK Page 743 #5-13 Show Work!

4. Pre-Algebra 6-7 Volume of Pyramids and Cones 6-7 Volume of Pyramids and Cones Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

5. Chapter 6-6 Lesson Quiz Find the volume of each figure to the nearest tenth. Use 3.14 for . 306 in 3 942 in 3 160.5 in 3 No; the volume would be quadrupled because you have to use the square of the radius to find the volume. 10 in. 8.5 in. 3 in. 12 in. 2 in. 15 in. 10.7 in. 1.3. 2. 4. Explain whether doubling the radius of the cylinder above will double the volume.

6. Pre-Algebra 6-7 Volume of Pyramids and Cones Warm Up 1. Find the volume of a rectangular prism that is 4 in. tall, 16 in. wide and 48 in deep. 2. A cylinder has a height of 4.2 m and a diameter of 0.6 m. To the nearest tenth of a cubic meter, what is the volume of the cylinder? Use 3.14 for . 3. A triangular prism’s base is an equilateral triangle. The sides of the equilateral triangle are 4 ft, and the height of the prism is 8 ft. To the nearest cubic foot, what is the volume of the prism? 3072 in 3 1.2 m 3 55.4 ft 3 Pre-Algebra 6-7 Volume of Pyramids and Cones

7. Pre-Algebra 6-7 Volume of Pyramids and Cones Problem of the Day A ream of paper (500 sheets) forms a rectangular prism 11 in. by 8.5 in. by 2 in. What is the volume of one sheet of paper? 0.374 in 3

8. Pre-Algebra 6-7 Volume of Pyramids and Cones Learning Goal Assignment Learn to find the volume of pyramids and cones.

9. Pre-Algebra 6-7 Volume of Pyramids and Cones Vocabulary pyramid cone

10. Pre-Algebra 6-7 Volume of Pyramids and Cones A pyramid is named for the shape of its base. The base is a polygon, and all of the other faces are triangles. 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.

11. Pre-Algebra 6-7 Volume of Pyramids and Cones VOLUME OF PYRAMIDS AND CONES (2 2 )

12. Pre-Algebra 6-7 Volume of Pyramids and Cones Additional Example 1A: Finding the Volume of Pyramids and Cones Find the volume of the figure. 1313 V = 14 6 V = 28 cm 3 A. V = Bh 1313 B = (4 7) = 14 cm 2 1212

13. Pre-Algebra 6-7 Volume of Pyramids and Cones Try This: Example 1A 1313 V = 17.5 7 V  40.8 in 3 A. V = Bh 1313 B = (5 7) = 17.5 in 2 1212 Find the volume of the figure. 5 in. 7 in.

14. Pre-Algebra 6-7 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 B. V = Bh 1313 B = (3 2 ) = 9 in 2 Use 3.14 for . Find the volume of the figure.

15. Pre-Algebra 6-7 Volume of Pyramids and Cones 1313 V = 9 7 V = 21  65.9 m 3 B. V = Bh 1313 B = (3 2 ) = 9 m 2 Use 3.14 for . Find the volume of the figure. Try This: Example 1B 7 m 3 m

16. Pre-Algebra 6-7 Volume of Pyramids and Cones Additional Example 1C: Finding the Volume of Pyramids and Cones 1313 V = 84 10 V = 280 m 3 C. V = Bh 1313 B = 14 6 = 84 m 2 Find the volume of the figure.

17. Pre-Algebra 6-7 Volume of Pyramids and Cones 1313 V = 16 8 V  42.7 ft 3 C. V = Bh 1313 B = 4 4 = 16 ft 2 Find the volume of the figure. Try This: Example 1C 4 ft 8 ft

18. Pre-Algebra 6-7 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.

19. Pre-Algebra 6-7 Volume of Pyramids and Cones Try This: 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. 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.

20. Pre-Algebra 6-7 Volume of Pyramids and Cones Additional Example 4: Social Studies Application The Pyramid of Kukulcán in Mexico is a square pyramid. Its height is 24 m and its base has 55 m sides. Find the volume of the pyramid. B = 55 2 = 3025 m 2 1313 V = (3025)(24) V = 24,200 m 3 A = bh V = Bh 1313

21. Pre-Algebra 6-7 Volume of Pyramids and Cones Try This: Example 4 B = 48 2 = 2304 m 2 1313 V = (2304)(12) V = 9216 m 3 A = bh V = Bh 1313 Find the volume of a pyramid with a height of 12 m and a base with 48 m sides.

22. Pre-Algebra 6-7 Volume of Pyramids and Cones Lesson Quiz: Part 1 Find the volume of each figure to the nearest tenth.Use 3.14 for . 78.5 in 3 6.3 m 3 1. the triangular pyramid 2. the cone

23. Pre-Algebra 6-7 Volume of Pyramids and Cones 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. 3. Explain whether tripling the height of a square pyramid would triple the volume.