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**7.5 Volume of Prisms and Cylinders**

MA 08Geometry 7.5 Volume of Prisms and Cylinders

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**Geometry 12.4 Volume of Prisms and Cylinders**

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

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**Geometry 12.4 Volume of Prisms and Cylinders**

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

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**Geometry 12.4 Volume of Prisms and Cylinders**

Cubic Unit V = s3 V = 1 cu. unit s 1 1 s 1 s Monday, May 5, 2:51 Geometry 12.4 Volume of Prisms and Cylinders

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**Geometry 12.4 Volume of Prisms and Cylinders**

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

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**Geometry 12.4 Volume of Prisms and Cylinders**

Cylinder: V = r2h r B h h V = Bh Monday, May 5, 2:51 Geometry 12.4 Volume of Prisms and Cylinders

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**Example 1 Find the volume.**

Triangular Prism V = Bh Base = 40 V = 40(3) = 120 10 8 3 Abase = ½ (10)(8) = 40 Monday, May 5, 2:51 Geometry 12.4 Volume of Prisms and Cylinders

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**Geometry 12.4 Volume of Prisms and Cylinders**

Example 3 A soda can measures 4.5 inches high and the diameter is 2.5 inches. Find the approximate volume. V = r2h V = (1.252)(4.5) V 22 in3 (The diameter is 2.5 in. The radius is 2.5 ÷ 2 inches.) Monday, May 5, 2:51 Geometry 12.4 Volume of Prisms and Cylinders

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**Geometry 12.4 Volume of Prisms and Cylinders**

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

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**Geometry 12.4 Volume of Prisms and Cylinders**

Example 4 Solution VTop = (42)(3) = 48 in3 VMid = (62)(4) = 144 in3 VBot = (72)(6) = 294 in3 r = 4 8 3 r = 6 12 4 486 in3 14 6 r = 7 Monday, May 5, 2:51 Geometry 12.4 Volume of Prisms and Cylinders

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**Geometry 12.4 Volume of Prisms and Cylinders**

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

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**Geometry 12.4 Volume of Prisms and Cylinders**

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. 48 44 52 Monday, May 5, 2:51 Geometry 12.4 Volume of Prisms and Cylinders

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**Geometry 12.4 Volume of Prisms and Cylinders**

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

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**Geometry 12.4 Volume of Prisms and Cylinders**

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: Aout = (242) = 576 Area of Inner Circle: Ain = (222) = 484 Area of Base (Ring): ABase = 576 - 484 = 92 48 44 52 Monday, May 5, 2:51 Geometry 12.4 Volume of Prisms and Cylinders

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**Geometry 12.4 Volume of Prisms and Cylinders**

Example 5 Solution V = Bh ABase = B = 92 V = (92)(52) V = 4784 V 15,021.8 in3 48 44 52 Monday, May 5, 2:51 Geometry 12.4 Volume of Prisms and Cylinders

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**Geometry 12.4 Volume of Prisms and Cylinders**

Example 6 4 5 L A metal bar has a volume of 2400 cm3. The sides of the base measure 4 cm by 5 cm. Determine the length of the bar. Monday, May 5, 2:51 Geometry 12.4 Volume of Prisms and Cylinders

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**Geometry 12.4 Volume of Prisms and Cylinders**

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

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**Geometry 12.4 Volume of Prisms and Cylinders**

Summary The volumes of prisms and cylinders are essentially the same: V = Bh & V = r2h 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. Monday, May 5, 2:51 Geometry 12.4 Volume of Prisms and Cylinders

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**Geometry 12.4 Volume of Prisms and Cylinders**

B h h V = r2h V = Bh These are on your reference sheet. Monday, May 5, 2:51 Geometry 12.4 Volume of Prisms and Cylinders

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**Geometry 12.4 Volume of Prisms and Cylinders**

Which Holds More? This one! 3.2 in 1.6 in 4 in 4.5 in 2.3 in Monday, May 5, 2:51 Geometry 12.4 Volume of Prisms and Cylinders

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**Geometry 12.4 Volume of Prisms and Cylinders**

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

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**Geometry 12.4 Volume of Prisms and Cylinders**

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

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**Geometry 12.4 Volume of Prisms and Cylinders**

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

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