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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 3 8-5 Volume of Prisms and Cylinders 9 ft 2 78.5 in 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 3 8-5 Volume of Prisms and Cylinders

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Learn to find the volume of prisms and cylinders. Course 3 8-5 Volume of Prisms and Cylinders TB P. 413-417

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Vocabulary cylinder prism Insert Lesson Title Here Course 3 8-5 Volume of Prisms and Cylinders

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Course 3 8-5 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 3 8-5 Volume of Prisms and Cylinders Height Triangular prism Rectangular prism Cylinder Base Height Base Height Base

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Course 3 8-5 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) = 24 75.4 units 3 V = Bh = (r 2 )h

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Course 3 8-5 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 3 8-5 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 3 8-5 Volume of Prisms and Cylinders 4 in. 12 in. = 192 602.9 in 3 B = (4 2 ) = 16 in 2 V = Bh = 16 12 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 3 8-5 Volume of Prisms and Cylinders 5 ft 7 ft 6 ft V = Bh = 15 7 = 105 ft 3 B = 6 5 = 15 ft 2 1212 Additional Example 1C: Finding the Volume of Prisms and Cylinders Area of base Volume of a prism

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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 3 8-5 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 3 8-5 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 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 3 8-5 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) = 452.16 ≈ 452 Use 3.14 for . The volume of the drum is approximately 452 in 3.

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Course 3 8-5 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 + 10,000 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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Lesson Quiz Find the volume of each figure to the nearest tenth. Use 3.14 for . 306 in 3 942 in 3 Insert Lesson Title Here 160.5 in 3 No; the volume would be quadrupled because you have to use the square of the radius to find the volume. Course 3 8-5 Volume of Prisms and Cylinders 10 in. 8.5 in. 3 in. 12 in. 2 in. 15 in. 10.7 in. 1.3. 2. 4. Explain whether doubling the radius of the cylinder above will double the volume.

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