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Preview Warm Up California Standards Lesson Presentation
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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 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
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Extension of MG2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders. California Standards
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The height of a pyramid or cone is measured from the highest point to the base along a perpendicular line.
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Additional Example 1: Finding the Volume of Pyramids and Cones
Find the volume of the figure. A. B = (4 • 7) = 14 cm2 1 2 1 3 V = • 14 • 6 V = Bh 1 3 V = 28 cm3
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Additional Example 1: Finding the Volume of Pyramids and Cones
Find the volume of the figure. Use 3.14 for p. B. B = (32) = 9 in2 1 3 V = • 9 • 10 V = Bh 1 3 V = 30 94.2 in3 Use 3.14 for .
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Check It Out! Example 1 Find the volume of the figure. A. B = (5 • 7) = 17.5 in2 1 2 7 in. 1 3 V = • 17.5 • 7 V = Bh 1 3 5 in. 7 in. V 40.8 in3
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Check It Out! Example 1 Find the volume of the figure. Use 3.14 for p. B. B = (32) = 9 m2 7 m 1 3 V = • 9 • 7 V = Bh 1 3 3 m V = 21 65.9 m3 Use 3.14 for .
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Additional Example 2: 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. Step 1: Find the area of the base. B = 552 The base is a square. = 3025 m2 Multiply.
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Additional Example 2 Continued
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. Step 2: Find the volume. 1 3 V = Bh Write the formula. 1 3 V = (3025)(24) Substitute for B and h. V = 24,200 m3 Multiply. The volume of the pyramid is 24,200 m3.
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Check It Out! Example 2 Find the volume of a pyramid with a height of 12 m and a base with 48 m sides. Step 1: Find the area of the base. B = 482 The base is a square. = 2304 m2 Multiply.
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Check It Out! Example 2 Continued
Find the volume of a pyramid with a height of 12 m and a base with 48 m sides. Step 2: Find the volume. 1 3 V = Bh Write the formula. 1 3 V = (2304)(12) Substitute for B and h. V ≈ 9216 m3 Multiply. The volume of the pyramid is 9,216 m3.
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Lesson Quiz: Part l 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
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Lesson Quiz: Part ll 3. Explain whether tripling the height of the triangular 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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