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Warm Up

86. 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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Warm Up

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  1. 86 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?

  2. 86 Volume of Pyramids and Cones Course 3 Insert Lesson Title Here Learning Target: to find the volume of pyramids and cones. Vocabulary pyramid cone

  3. 86 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.

  4. 86 Volume of Pyramids and Cones VOLUME OF PYRAMIDS AND CONES (22) Course 3

  5. 86 Volume of Pyramids and Cones B = (4 • 7) = 14 cm2 1 3 1 2 1 3 V = Bh V = • 14 • 6 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 1A: Finding the Volume of Pyramids and Cones Find the volume of the figure. Use 3.14 for p. V = 28 cm3

  6. 86 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 .

  7. 86 Volume of Pyramids and Cones B = (__ • __ ) = ____ 1 3 1 2 1 3 V = Bh V = • __ • __ 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  ___ in3

  8. 86 Volume of Pyramids and Cones 1 3 1 3 V = Bh V = • __• __ Course 3 Check It Out: Example 1B Find the volume of the figure. Use 3.14 for p. B = (r2) = ___ m2 7 m 3 m V = ____ m3 Use 3.14 for .

  9. 86 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.

  10. 86 Volume of Pyramids and Cones 1 3 1 3 V = (3025)(24) V = Bh 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

  11. 86 Volume of Pyramids and Cones Course 3 Insert Lesson Title Here Lesson Quiz Find the volume of each figure to the nearest tenth. Use 3.14 for p. 1. the triangular pyramid 2. the cone

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