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8-5 Volume of Prisms and Cylinders Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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Warm Up Find the area of each figure described. Use 3.14 for. 1. a triangle with a base of 6 feet and a height of 3 feet 2. a circle with radius 5 in. Course Volume of Prisms and Cylinders 9 ft ft 2

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Problem of the Day You are painting identical wooden cubes red and blue. Each cube must have 3 red faces and 3 blue faces. How many cubes can you paint that can be distinguished from one another? only 2 Course Volume of Prisms and Cylinders

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Learn to find the volume of prisms and cylinders. Course Volume of Prisms and Cylinders

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Vocabulary cylinder prism Insert Lesson Title Here Course Volume of Prisms and Cylinders

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Course Volume of Prisms and Cylinders A cylinder is a three-dimensional figure that has two congruent circular bases. 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.

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Course Volume of Prisms and Cylinders Height Triangular prism Rectangular prism Cylinder Base Height Base Height Base

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Course 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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Course Volume of Prisms and Cylinders Area is measured in square units. Volume is measured in cubic units. Remember!

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Find the volume of each figure to the nearest tenth. Use 3.14 for. Additional Example 1A: Finding the Volume of Prisms and Cylinders Course Volume of Prisms and Cylinders 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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Find the volume of the figure to the nearest tenth. Use 3.14 for. Course Volume of Prisms and Cylinders 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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Find the volume of the figure to the nearest tenth. Use 3.14 for. Course Volume of Prisms and Cylinders 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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Find the volume of the figure to the nearest tenth. Use 3.14 for. Course Volume of Prisms and Cylinders 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 Check It Out: Example 1A

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Find the volume of the figure to the nearest tenth. Use 3.14 for. Course Volume of Prisms and Cylinders 8 cm 15 cm B = (8 2 ) = 64 cm 2 = (64)(15) = 960 3,014.4 cm 3 Check It Out: Example 1B Area of base Volume of a cylinder V = Bh

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Find the volume of the figure to the nearest tenth. Use 3.14 for. Course Volume of Prisms and Cylinders 10 ft 14 ft 12 ft = 60 ft 2 = 60(14) = 840 ft 3 Check It Out: Example 1C Area of base Volume of a prism B = V = Bh

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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 Course Volume of Prisms and Cylinders 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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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 Course Volume of Prisms and Cylinders 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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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. Check It Out: Example 2A Course Volume of Prisms and Cylinders 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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Course Volume of Prisms and Cylinders Check It Out: Example 2A Continued 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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Course Volume of Prisms and Cylinders Check It Out: Example 2A Continued 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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Course 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. Check It Out: Example 2B V = 36 3 = 108 cm 3 The original cylinder has a volume of 4 3 = 12 cm 3.

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Check It Out: Example 2B Continued Course Volume of Prisms and Cylinders 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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A drum company advertises a snare drum that is 4 inches high and 12 inches in diameter. Estimate the volume of the drum. Additional Example 3: Music Application Course Volume of Prisms and Cylinders d = 12, h = 4 r = = = 6 Volume of a cylinder. d2d2 V = (r 2 )h 12 2 = (3.14)(6) 2 4 = (3.14)(36)(4) = Use 3.14 for. The volume of the drum is approximately 452 in. 2

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A drum company advertises a bass drum that is 12 inches high and 28 inches in diameter. Estimate the volume of the drum. Check It Out: Example 3 Course Volume of Prisms and Cylinders d = 28, h = 12 r = = = 14 Volume of a cylinder. d2d2 V = (r 2 )h 28 2 = (3.14)(14) 2 12 = (3.14)(196)(12) = ,385 Use 3.14 for. The volume of the drum is approximately 7,385 in. 2

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Course Volume of Prisms and Cylinders 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. Additional Example 4: Finding the Volume of Composite Figures

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Check It Out: Example 4 Course Volume of Prisms and Cylinders Find the volume of the house. 3 ft 4 ft 8 ft 5 ft = (8)(3)(4) + (5)(8)(3) 1212 = V = 156 ft 3 Volume of house Volume of rectangular prism Volume of triangular prism + =

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Lesson Quiz Find the volume of each figure to the nearest tenth. Use 3.14 for. 306 in in 3 Insert Lesson Title Here in 3 No; the volume would be quadrupled because you have to use the square of the radius to find the volume. Course Volume of Prisms and Cylinders 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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