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Warm Up

Warm Up. Problem of the Day. Lesson Presentation. Lesson Quizzes. 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

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Warm Up

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  1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

  2. 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

  3. Problem of the Day How can you cut the rectangular prism into 8 pieces of equal volume by making only 3 straight cuts?

  4. Sunshine State Standards MA.7.G.2.1 Justify and apply formulas for… volume of…prisms [and] cylinders… Also MA.7.G.2.2

  5. Vocabulary volume

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

  7. To find the volume of a rectangular prism, you can count cubes or multiply the lengths of the edges.

  8. Additional Example 1A: Using a Formula to Find the Volume of a Prism Find the volume of the figure. V = Bh Use the formula. The base is a square: B = 4 4 =16. V = 1612 Substitute for B and h. V = 192 Multiply. The volume of the prism is 192 ft3.

  9. Additional Example 1B: Using a Formula to Find the Volume of a Prism Find the volume of the figure. V = Bh Use the formula. The base is a triangle: B = 1/2 16 6 =48. V = 488 Substitute for B and h. V = 384 Multiply. The volume of the triangular prism is 384 yd3.

  10. Check It Out: Example 1A Find the volume of each figure to the nearest tenth. b = 6.3(8) = 50.4 V = Bh = 50.4(6.3) = 317.52 ≈ 317.5 ft3.

  11. Check It Out: Example 1B Find the volume of each figure to the nearest tenth. V = Bh 1 2 B = (13)(10) = 65 V = (65)(50) = 3250 ≈ 3250 m3.

  12. Reading Math Any unit of measurement with an exponent of 3 is a cubic unit. For example, m3 means “cubic meter” and in3 means “cubic inch.”

  13. Finding the volume of a cylinder is similar to finding the volume of a prism.

  14. Additional Example 2: Using a Formula to Find the Volume of a Cylinder A can of tuna is shaped like a cylinder. Find its volume to the nearest tenth. Use 3.14 for . V = r2h Use the formula. The radius of the cylinder is 5 m, and the height is 4.2 m Substitute for r and h. V 3.14 · 52 · 4.2 Multiply. V  329.7 The volume is about 329.7 m3.

  15. Check It Out: Example 2 Find the volume of the cylinder to the nearest tenth. Use 3.14 for. 7 ft 3.8 ft V = r2h  (3.14)(7)2(3.8)  584.668  584.7 ft3.

  16. Additional Example 3: Finding The Volume of a Composite Figure Find the volume of the composite figure to the nearest ft. Use 3.14 for . Volume of a composite figure Volume of triangular prism Volume of prism + = + = Bh Bh V V (4)(6)(12) + (½)(4)(6) · (6)‏ V 288 + 72 V 360 ft3

  17. Check It Out: Example 3A 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. V Bh +  r2h 317.5 + 584.7 902.2 902.2 ft3

  18. Check It Out: Example 3B 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 . V Bh +  r2h 1 2 B (8)(5) = 20 V  (20)(10) + (3.14)(6)2 (4)  652.16 652.2 m3

  19. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  20. Lesson Quiz 1. Find the volume of the prism. 792 cm3 2. A storage tank is shaped like a cylinder. Find its volume to the nearest tenth. Use 3.14 for . 4,069.4 cm3 3. Find the volume of the composite figure. 216 in3

  21. Lesson Quiz for Student Response Systems 1. Identify the volume of the prism. A. 35 cm3 B. 95 cm3 C. 133 cm3 D. 665 cm3

  22. Lesson Quiz for Student Response Systems 2. A piece of wood is shaped like a cylinder. Find its volume to the nearest tenth. Use 3.14 for . A. 5849.8 cm3 B. 1950 cm3 C. 414 cm3 D. 207 cm3

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