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MA 08Geometry 7.5 Volume of Prisms and Cylinders.

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Presentation on theme: "MA 08Geometry 7.5 Volume of Prisms and Cylinders."— Presentation transcript:

1 MA 08Geometry 7.5 Volume of Prisms and Cylinders

2 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.

3 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

4 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

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

6 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

7 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

8 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.)

9 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.

10 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

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

12 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

13 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

14 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

15 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

16 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

17 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

18 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.

19 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.

20 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!

21 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

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

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


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