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MA 08Geometry 7.5 Volume of Prisms and Cylinders

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Geometry 12.4 Volume of Prisms and Cylinders 2 Monday, May 5, 2:51 Goals Find the volume of prisms. Find the volume of cylinders. Solve problems using volume.

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Geometry 12.4 Volume of Prisms and Cylinders 3 Monday, May 5, 2:51 Volume The number of cubic units contained in a solid. Measured in cubic units. Basic Formula: V = Bh B = area of the base, h = height

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Geometry 12.4 Volume of Prisms and Cylinders 4 Monday, May 5, 2:51 Cubic Unit 1 1 1 V = 1 cu. unit s s s V = s 3

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Geometry 12.4 Volume of Prisms and Cylinders 5 Monday, May 5, 2:51 B B B h h h Prism: V = Bh

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Geometry 12.4 Volume of Prisms and Cylinders 6 Monday, May 5, 2:51 Cylinder: V = r 2 h B h r h V = Bh

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Geometry 12.4 Volume of Prisms and Cylinders 7 Monday, May 5, 2:51 Example 1Find the volume. 10 8 3 Triangular Prism V = Bh Base = 40 V = 40(3) = 120 A base = ½ (10)(8) = 40

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Geometry 12.4 Volume of Prisms and Cylinders 8 Monday, May 5, 2:51 Example 3 A soda can measures 4.5 inches high and the diameter is 2.5 inches. Find the approximate volume. V = r 2 h V = (1.25 2 )(4.5) V 22 in 3 (The diameter is 2.5 in. The radius is 2.5 ÷ 2 inches.)

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Geometry 12.4 Volume of Prisms and Cylinders 9 Monday, May 5, 2:51 Example 4 A wedding cake has three layers. The top cake has a diameter of 8 inches, and is 3 inches deep. The middle cake is 12 inches in diameter, and is 4 inches deep. The bottom cake is 14 inches in diameter and is 6 inches deep. Find the volume of the entire cake, ignoring the icing.

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Geometry 12.4 Volume of Prisms and Cylinders 10 Monday, May 5, 2:51 Example 4 Solution 8 12 14 3 4 6 r = 4 r = 6 r = 7 V Top = (4 2 )(3) = 48 150.8 in 3 V Mid = (6 2 )(4) = 144 452.4 in 3 V Bot = (7 2 )(6) = 294 923.6 in 3 486 1526.8 in 3

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Geometry 12.4 Volume of Prisms and Cylinders 11 Monday, May 5, 2:51

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Geometry 12.4 Volume of Prisms and Cylinders 12 Monday, May 5, 2:51 Example 5 A manufacturer of concrete sewer pipe makes a pipe segment that has an outside diameter (o.d.) of 48 inches, an inside diameter (i.d.) of 44 inches, and a length of 52 inches. Determine the volume of concrete needed to make one pipe segment. 44 48 52

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Geometry 12.4 Volume of Prisms and Cylinders 13 Monday, May 5, 2:51 Example 5 Solution Strategy: Find the area of the ring at the top, which is the area of the base, B, and multiply by the height. View of the Base

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Geometry 12.4 Volume of Prisms and Cylinders 14 Monday, May 5, 2:51 Example 5 Solution Strategy: Find the area of the ring at the top, which is the area of the base, B, and multiply by the height. Area of Outer Circle: A out = (24 2 ) = 576 Area of Inner Circle: A in = (22 2 ) = 484 Area of Base (Ring): A Base = 576 - 484 = 92 44 48 52

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Geometry 12.4 Volume of Prisms and Cylinders 15 Monday, May 5, 2:51 Example 5 Solution V = Bh A Base = B = 92 V = (92 )(52) V = 4784 V 15,021.8 in 3 44 48 52

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Geometry 12.4 Volume of Prisms and Cylinders 16 Monday, May 5, 2:51 Example 6 A metal bar has a volume of 2400 cm 3. The sides of the base measure 4 cm by 5 cm. Determine the length of the bar. 4 5 L

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Geometry 12.4 Volume of Prisms and Cylinders 17 Monday, May 5, 2:51 Example 6 Solution V = L W H 2400 = L 4 5 2400 = 20L L = 120 cm 4 5 L

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Geometry 12.4 Volume of Prisms and Cylinders 18 Monday, May 5, 2:51 Summary The volumes of prisms and cylinders are essentially the same: V = Bh &V = r 2 h where B is the area of the base, h is the height of the prism or cylinder. Use what you already know about area of polygons and circles for B.

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Geometry 12.4 Volume of Prisms and Cylinders 19 Monday, May 5, 2:51 V = Bh V = r 2 h B h h r These are on your reference sheet.

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Geometry 12.4 Volume of Prisms and Cylinders 20 Monday, May 5, 2:51 Which Holds More? 3.2 in1.6 in 4 in4.5 in 2.3 in This one!

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Geometry 12.4 Volume of Prisms and Cylinders 21 Monday, May 5, 2:51 What would the height of cylinder 2 have to be to have the same volume as cylinder 1? r = 4 h r = 3 8 #1 #2

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Geometry 12.4 Volume of Prisms and Cylinders 22 Monday, May 5, 2:51 Solution r = 4 8 #1

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Geometry 12.4 Volume of Prisms and Cylinders 23 Monday, May 5, 2:51 Solution h r = 3 #2

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