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8-6

8-6. Volume of Pyramids and Cones. Warm Up. Problem of the Day. Lesson Presentation. Course 3. 8-6. Volume of Pyramids and Cones. Course 3. Warm Up 1. Find the volume of a rectangular prism that is 4 in. tall, 16 in. wide, and 48 in deep.

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  1. 8-6 Volume of Pyramids and Cones Warm Up Problem of the Day Lesson Presentation Course 3

  2. 8-6 Volume of Pyramids and Cones Course 3 • 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 p. • 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 in3 1.2 m3 55.4 ft3

  3. 8-6 Volume of Pyramids and Cones Course 3 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 in3

  4. 8-6 Volume of Pyramids and Cones Course 3 Learn to find the volume of pyramids and cones.

  5. 8-6 Volume of Pyramids and Cones Course 3 Insert Lesson Title Here Vocabulary pyramid cone

  6. 8-6 Volume of Pyramids and Cones Course 3 Insert Lesson Title Here 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.

  7. 8-6 Volume of Pyramids and Cones VOLUME OF PYRAMIDS AND CONES (22) Course 3

  8. 8-6 Volume of Pyramids and Cones B = (4 • 7) = 14 cm2 1 3 1 2 1 3 V = Bh V = • 14 • 6 Course 3 Additional Example 1A: Finding the Volume of Pyramids and Cones Find the volume of the figure. Use 3.14 for p. V = 28 cm3

  9. 8-6 Volume of Pyramids and Cones 1 3 1 3 V = Bh V = • 9 • 10 Course 3 Additional Example 1B: Finding the Volume of Pyramids and Cones Find the volume of the figure. Use 3.14 for p. B = (32) = 9 in2 V = 30 94.2 in3 Use 3.14 for .

  10. 8-6 Volume of Pyramids and Cones B = (5 • 7) = 17.5 in2 1 3 1 2 1 3 V = Bh V = • 17.5 • 7 Course 3 Check It Out: Example 1A Find the volume of the figure. Use 3.14 for p. 7 in. 5 in. 7 in. V  40.8 in3

  11. 8-6 Volume of Pyramids and Cones 1 3 1 3 V = Bh V = • 9 • 7 Course 3 Check It Out: Example 1B Find the volume of the figure. Use 3.14 for p. B = (32) = 9 m2 7 m 3 m V = 21 65.9 m3 Use 3.14 for .

  12. 8-6 Volume of Pyramids and Cones Course 3 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.

  13. 8-6 Volume of Pyramids and Cones Original Dimensions Double the Height Double the Radius 1 3 V = pr2 (2h) V = pr2h V = p (2r)2h 1 3 1 3 1 3 = p(2 • 2)2(5) = p(22)(2•5) = p(22)5 1 3 1 3  20.93 m3  41.87 m3  83.73 m3 Course 3 Insert Lesson Title Here 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. 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.

  14. 8-6 Volume of Pyramids and Cones 1 3 1 3 V = (3025)(24) V = Bh Caution! A lowercase b is used to represent the length of the base of a two-dimensional figure. A capitol B is used to represent the area of the base of a solid figure. Course 3 Additional Example 3: 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 = 552 = 3025 m2 A = bh V = 24,200 m3

  15. 8-6 Volume of Pyramids and Cones 1 3 1 3 V = (2304)(12) V = Bh Course 3 Insert Lesson Title Here Check It Out: Example 3 Find the volume of a pyramid with a height of 12 m and a base with 48 m sides. B = 482 = 2304 m2 A = bh V = 9216 m3

  16. 8-6 Volume of Pyramids and Cones 1 3 V = Bh Course 3 Additional Example 4: Using a Calculator to Find Volume Use a calculator to find the volume of a cone to the nearest cubic centimeter if the radius of the base is 15 cm and the height is 64 cm. Use the pi button on your calculator to find the area of the base. p B = pr2 15 2ND ^  X2 ENTER Next, with the area of the base still displayed, find the volume of the cone. 64 1 3 ENTER   ( ) ÷ The volume of the cone is approximately 15,080 cm3.

  17. 8-6 Volume of Pyramids and Cones 1 3 V = Bh Course 3 Check It Out: Example 4 Use a calculator to find the volume of a cone to the nearest cubic centimeter if the radius of the base is 14 cm and the height is 16 cm. Use the pi button on your calculator to find the area of the base. p B = pr2 14 2ND ^  X2 ENTER Next, with the area of the base still displayed, find the volume of the cone. 16 1 3 ENTER   ( ) ÷ The volume of the cone is approximately 3,282 cm3.

  18. 8-6 Volume of Pyramids and Cones Course 3 Insert Lesson Title Here Lesson Quiz: Part 1 Find the volume of each figure to the nearest tenth. Use 3.14 for p. 1. the triangular pyramid 6.3 m3 2. the cone 78.5 in3

  19. Volume of Pyramids and Cones 8-6 Course 3 Insert Lesson Title Here Lesson Quiz: Part 2 Find the volume of each figure to the nearest tenth. Use 3.14 for p. 3. Explain whether tripling the height of a square pyramid would triple the volume. 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.

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