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8-8 Volume of Prisms and Cylinders Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

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8-8 Volume of Prisms and Cylinders Warm Up Identify the figure described. 1. two triangular faces and the other faces in the shape of parallelograms 2. one hexagonal base and the other faces in the shape of triangles 3. one circular base and a curved lateral surface that forms a vertex triangular prism hexagonal pyramid cone

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8-8 Volume of Prisms and Cylinders Problem of the Day How can you cut the rectangular prism into 8 pieces of equal volume by making only 3 straight cuts?

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8-8 Volume of Prisms and Cylinders MA.7.G.2.1 Justify and apply formulas for… volume of…prisms [and] cylinders… Also MA.7.G.2.2 Sunshine State Standards

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8-8 Volume of Prisms and Cylinders Vocabulary volume

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8-8 Volume of Prisms and Cylinders Any three-dimensional figure can be filled completely with congruent cubes and parts of cubes. The volume of a three-dimensional figure is the number of cubes it can hold. Each cube represents a unit of measure called a cubic unit.

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8-8 Volume of Prisms and Cylinders To find the volume of a rectangular prism, you can count cubes or multiply the lengths of the edges.

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8-8 Volume of Prisms and Cylinders

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8-8 Volume of Prisms and Cylinders Find the volume of the figure. Additional Example 1A: Using a Formula to Find the Volume of a Prism V = Bh The volume of the prism is 192 ft 3. Use the formula. The base is a square: B = 4 4 = 16. V = 16 12 Substitute for B and h. Multiply.V = 192

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8-8 Volume of Prisms and Cylinders Find the volume of the figure. Additional Example 1B: Using a Formula to Find the Volume of a Prism V = Bh The volume of the triangular prism is 384 yd 3. Use the formula. The base is a triangle: B = 1/2 16 6 = 48. V = 48 8 Substitute for B and h. Multiply.V = 384

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8-8 Volume of Prisms and Cylinders Find the volume of each figure to the nearest tenth. Check It Out: Example 1A b = 6.3(8) = 50.4 V = Bh = 50.4(6.3) = 317.52 ≈ 317.5 ft 3.

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8-8 Volume of Prisms and Cylinders Find the volume of each figure to the nearest tenth. Check It Out: Example 1B V = Bh 1212 B = (13)(10) = 65 V = (65)(50) = 3250 ≈ 3250 m 3.

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8-8 Volume of Prisms and Cylinders Any unit of measurement with an exponent of 3 is a cubic unit. For example, m 3 means “cubic meter” and in 3 means “cubic inch.” Reading Math

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8-8 Volume of Prisms and Cylinders Finding the volume of a cylinder is similar to finding the volume of a prism.

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8-8 Volume of Prisms and Cylinders A can of tuna is shaped like a cylinder. Find its volume to the nearest tenth. Use 3.14 for . Additional Example 2: Using a Formula to Find the Volume of a Cylinder V = r 2 h The radius of the cylinder is 5 m, and the height is 4.2 m V 3.14 · 5 2 · 4.2 V 329.7 The volume is about 329.7 m 3. Use the formula. Substitute for r and h. Multiply.

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8-8 Volume of Prisms and Cylinders Check It Out: Example 2 V = r 2 h (3.14)(7) 2 (3.8) 584.7 ft 3. Find the volume of the cylinder to the nearest tenth. Use 3.14 for . 3.8 ft 7 ft 584.668

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8-8 Volume of Prisms and Cylinders Find the volume of the composite figure to the nearest ft. Use 3.14 for Additional Example 3: Finding The Volume of a Composite Figure Volume of a composite figure Volume of prism = + Volume of triangular prism V = + Bh V (4)(6)(12) + (½)(4)(6) · (6) V 288 + 72 V 360 ft 3

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8-8 Volume of Prisms and Cylinders Assume that the prism from Exercise 1a has been stacked on top of the cylinder from Exercise 2. Find the volume of the composite figure to the nearest tenth. Use 3.14 for Check It Out: Example 3A V Bh + r 2 h 317.5 + 584.7 902.2 902.2 ft 3

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8-8 Volume of Prisms and Cylinders The triangular faces of a triangular prism have a height of 5 m and a base of 8 m. The height of the prism is 10 m. The triangular prism is connected to a cylinder. The height of the cylinder is 4 m and the radius is 6 m. Find the volume of the composite figure to the nearest tenth. Use 3.14 for . Check It Out: Example 3B V Bh + r 2 h B (8)(5) = 20 652.2 m 3 1212 V (20)(10) + (3.14)(6) 2 (4) 652.16

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8-8 Volume of Prisms and Cylinders Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

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8-8 Volume of Prisms and Cylinders Lesson Quiz 1. Find the volume of the prism. 4,069.4 cm 3 2. A storage tank is shaped like a cylinder. Find its volume to the nearest tenth. Use 3.14 for 792 cm 3 3. Find the volume of the composite figure. 216 in 3

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8-8 Volume of Prisms and Cylinders 1. Identify the volume of the prism. A. 35 cm 3 B. 95 cm 3 C. 133 cm 3 D. 665 cm 3 Lesson Quiz for Student Response Systems

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8-8 Volume of Prisms and Cylinders 2. A piece of wood is shaped like a cylinder. Find its volume to the nearest tenth. Use 3.14 for A. 5849.8 cm 3 B. 1950 cm 3 C. 414 cm 3 D. 207 cm 3 Lesson Quiz for Student Response Systems

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