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Surface Area & Volume

Lesson 17. Surface Area & Volume. Volume of Prisms. Warm-Up. Find the area of each figure. What do you know about volume? List at least 3 things. Volume of Prisms. Target: Calculate the volume of prisms. Vocabulary. Volume: The number of cubic units needed to fill a solid.

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Surface Area & Volume

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  1. Lesson 17 Surface Area & Volume Volume of Prisms

  2. Warm-Up Find the area of each figure. • What do you know about volume? List at least 3 things.

  3. Volume of Prisms Target: Calculate the volume of prisms.

  4. Vocabulary • Volume: The number of cubic units needed to fill a solid.

  5. Prism Volume The volume of a prism is equal to the product of the area of the base (B) and the height (h). Volume = (area of the base)(height) V = Bh

  6. Example 1a Find the volume of the prism. • V = Bh • V = (6 • 4)(12) • V = (24)(12) • V = 288 • Volume = 288 cm³

  7. Example 1b Find the volume of the prism. The base area is 41 cm2. • V = Bh • V = (41)(10) • V = 410 • Volume = 410 cm³

  8. Example 1c Find the volume of the prism. • V = Bh • V = ( • 8 • 3)(5.7) • V = (12)(5.7) • V = 68.4 • Volume = 68.4 m³

  9. Example 2 Mischa can buy her favorite laundry detergent in two different shaped containers. One container is a triangular prism with a base area of 15 square inches and a height of 6 inches. She can also buy the detergent in a rectangular prism container with a length of 5 inches, a width of 4 inches and a height of 4.5 inches. Which container has the most volume? • Triangular box Rectangular box V = Bh V = (15)(6) = 90 V = Bh V = (5 • 4)(4.5) = (20)(4.5) = 90 Both boxes are the same size – 90 cubic inches!

  10. Exit Problems • Find the volume of the prism. • A cereal box is a rectangular prism. It is 10 inches long, 14 inches tall and 3 inches wide. Find the volume of the cereal box.

  11. Communication Prompt • What type of prism is easiest for you to find the volume of? What type of prism is most difficult for you to find the volume of? Explain. • Explain how the formula on the Oregon State Assessment Formula sheet (lwh) and Bh are the same.

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