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Pre-Algebra 6-6 Volume of Prisms and Cylinders 6-6 Volume of Prisms and Cylinders Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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Pre-Algebra 6-6 Volume of Prisms and Cylinders Learn to find the volume of prisms and cylinders.

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Pre-Algebra 6-6 Volume of Prisms and Cylinders Vocabulary prism cylinder

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Pre-Algebra 6-6 Volume of Prisms and Cylinders A prism is a three-dimensional figure named for the shape of its bases. The two bases are congruent polygons. All of the other faces are parallelograms. A cylinder has two circular bases.

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Pre-Algebra 6-6 Volume of Prisms and Cylinders If all six faces of a rectangular prism are squares, it is a cube. Remember! Height Triangular prism Rectangular prism Cylinder Base Height Base Height Base

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Pre-Algebra 6-6 Volume of Prisms and Cylinders VOLUME OF PRISMS AND CYLINDERS WordsNumbersFormula Prism: The volume V of a prism is the area of the base B times the height h. Cylinder: The volume of a cylinder is the area of the base B times the height h. B = 2(5) = 10 units 2 V = 10(3) = 30 units 3 B = (2 2 ) = 4 units 2 V = (4)(6) = units 3 V = Bh = (r 2 )h

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Pre-Algebra 6-6 Volume of Prisms and Cylinders Area is measured in square units. Volume is measured in cubic units. Helpful Hint

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Pre-Algebra 6-6 Volume of Prisms and Cylinders Find the volume of each figure to the nearest tenth. Additional Example 1A: Finding the Volume of Prisms and Cylinders A. A rectangular prism with base 2 cm by 5 cm and height 3 cm. = 30 cm 3 B = 2 5 = 10 cm 2 V = Bh = 10 3 Area of base Volume of a prism

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Pre-Algebra 6-6 Volume of Prisms and Cylinders Find the volume of the figure to the nearest tenth. B. 4 in. 12 in. = in 3 B = (4 2 ) = 16 in 2 V = Bh = Additional Example 1B: Finding the Volume of Prisms and Cylinders Area of base Volume of a cylinder

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Pre-Algebra 6-6 Volume of Prisms and Cylinders Find the volume of the figure to the nearest tenth. C. 5 ft 7 ft 6 ft V = Bh = 15 7 = 105 ft 3 B = 6 5 = 15 ft Additional Example 1C: Finding the Volume of Prisms and Cylinders Area of base Volume of a prism

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Pre-Algebra 6-6 Volume of Prisms and Cylinders Find the volume of the figure to the nearest tenth. A. A rectangular prism with base 5 mm by 9 mm and height 6 mm. = 270 mm 3 B = 5 9 = 45 mm 2 V = Bh = 45 6 Area of base Volume of prism Try This: Example 1A

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Pre-Algebra 6-6 Volume of Prisms and Cylinders Find the volume of the figure to the nearest tenth. B. 8 cm 15 cm B = (8 2 ) = 64 cm 2 = (64)(15) = 960 3,014.4 cm 3 Try This: Example 1B Area of base Volume of a cylinder V = Bh

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Pre-Algebra 6-6 Volume of Prisms and Cylinders Find the volume of the figure to the nearest tenth. C. 10 ft 14 ft 12 ft = 60 ft 2 = 60(14) = 840 ft 3 Try This: Example 1C Area of base Volume of a prism B = V = Bh

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Pre-Algebra 6-6 Volume of Prisms and Cylinders A juice box measures 3 in. by 2 in. by 4 in. Explain whether tripling the length, width, or height of the box would triple the amount of juice the box holds. Additional Example 2A: Exploring the Effects of Changing Dimensions The original box has a volume of 24 in 3. You could triple the volume to 72 in 3 by tripling any one of the dimensions. So tripling the length, width, or height would triple the amount of juice the box holds.

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Pre-Algebra 6-6 Volume of Prisms and Cylinders A juice can has a radius of 2 in. and a height of 5 in. Explain whether tripling the height of the can would have the same effect on the volume as tripling the radius. Additional Example 2B: Exploring the Effects of Changing Dimensions By tripling the height, you would triple the volume. By tripling the radius, you would increase the volume to nine times the original.

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Pre-Algebra 6-6 Volume of Prisms and Cylinders A box measures 5 in. by 3 in. by 7 in. Explain whether tripling the length, width, or height of the box would triple the volume of the box. Try This: Example 2A Tripling the length would triple the volume. V = (15)(3)(7) = 315 cm 3 The original box has a volume of (5)(3)(7) = 105 cm 3.

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Pre-Algebra 6-6 Volume of Prisms and Cylinders A box measures 5 in. by 3 in. by 7 in. Explain whether tripling the length, width, or height of the box would triple the volume of the box. Try This: Example 2A The original box has a volume of (5)(3)(7) = 105 cm 3. Tripling the height would triple the volume. V = (5)(3)(21) = 315 cm 3

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Pre-Algebra 6-6 Volume of Prisms and Cylinders A box measures 5 in. by 3 in. by 7 in. Explain whether tripling the length, width, or height of the box would triple the volume of the box. Try This: Example 2A Tripling the width would triple the volume. V = (5)(9)(7) = 315 cm 3 The original box has a volume of (5)(3)(7) = 105 cm 3.

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Pre-Algebra 6-6 Volume of Prisms and Cylinders By tripling the radius, you would increase the volume nine times. A cylinder measures 3 cm tall with a radius of 2 cm. Explain whether tripling the radius or height of the cylinder would triple the amount of volume. Try This: Example 2B V = 36 3 = 108 cm 3 The original cylinder has a volume of 4 3 = 12 cm 3.

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Pre-Algebra 6-6 Volume of Prisms and Cylinders A cylinder measures 3 cm tall with a radius of 2 cm. Explain whether tripling the radius or height of the cylinder would triple the amount of volume. Try This: Example 2B Tripling the height would triple the volume. V = 4 9 = 36 cm 3 The original cylinder has a volume of 4 3 = 12 cm 3.

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Pre-Algebra 6-6 Volume of Prisms and Cylinders A section of an airport runway is a rectangular prism measuring 2 feet thick, 100 feet wide, and 1.5 miles long. What is the volume of material that was needed to build the runway? Additional Example 3: Construction Application length = 1.5 mi = 1.5(5280) ft = 7920 ft height = 2 ft = 1,584,000 ft 3 The volume of material needed to build the runway was 1,584,000 ft 3. width = 100 ft V = ft 3

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Pre-Algebra 6-6 Volume of Prisms and Cylinders A cement truck has a capacity of 9 yards 3 of concrete mix. How many truck loads of concrete to the nearest tenth would it take to pour a concrete slab 1 ft thick by 200 ft long by 100 ft wide? Try This: Example 3 V = 20,000(1) B = 200(100) = 20,000 ft 2 = 20,000 ft 3 27 ft 3 = 1 yd 3 20, yd = 82.3 Truck loads

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Pre-Algebra 6-6 Volume of Prisms and Cylinders Additional Example 4: Finding the Volume of Composite Figures Find the volume of the the barn. Volume of barn Volume of rectangular prism Volume of triangular prism + = = 30, ,000 V = (40)(50)(15) + (40)(10)(50) 1212 = 40,000 ft 3 The volume is 40,000 ft 3.

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Pre-Algebra 6-6 Volume of Prisms and Cylinders Try This: Example 4 Find the volume of the figure. 3 ft 4 ft 8 ft 5 ft = (8)(3)(4) + (5)(8)(3) 1212 = V = 156 ft 3 Volume of barn Volume of rectangular prism Volume of triangular prism + =

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Pre-Algebra 6-6 Volume of Prisms and Cylinders Challenge: A 6 cm section of plastic water pipe has inner diameter 12 cm and outer diameter 15 cm. Find the volume of the plastic pipe, not the hollow interior, to the nearest tenth.

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Pre-Algebra 6-6 Volume of Prisms and Cylinders Lesson Quiz Find the volume of each figure to the nearest tenth. Use 3.14 for. 306 in in 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 in Explain whether doubling the radius of the cylinder above will double the volume.

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