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Volume Prisms and Cylinders Lesson 12.4

Volume Prisms and Cylinders Lesson 12.4. Volume of a solid is the number of cubic units of space contained by the solid . The volume of a right rectangular prism is equal to the product of its length, its width, and its height. V = l wh. Find the volume of the rectangular prism.

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Volume Prisms and Cylinders Lesson 12.4

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  1. Volume Prisms and CylindersLesson 12.4

  2. Volume of a solid is the number of cubic units of space contained by the solid. • The volume of a right rectangular prism is equal to the product of its length, its width, and its height. • V = lwh

  3. Find the volume of the rectangular prism. V = lwh V = 14(7)(4) V = 392 m2 4m 7m 14m

  4. Theorem 115:The volume of a right rectangular prism is equal to the product of the height and the area of the base.V = Bh, where B is the area of the base. Find the height of the rectangular prism: V = Bh 3300 = 300h 11 = h V = 3300 B = 300 h

  5. Find the volume of any figure. Theorem 116: The volume of any prism is equal to the product of the height and the area of the base. V = Bh

  6. Theorem 117: The volume of a cylinder is equal to the product of the height and the area of the base. V = Bh V = Лr2h Find the volume of the cylinder. V = Лr2h V = Л42(24) V = 384Л in3 24in d = 8in

  7. Cross-Section of a prism or cylinder. A cross section is the intersection of a solid with a plane. Theorem 118:The volume of a prism or a cylinder is equal to the product of the figure’s cross sectional area and its height. V = ₵h, where ₵ is the area of the cross section.

  8. Find the volume of the triangular prism. V = Bh Find the area of the base. Base = ½ bh = ½ (12)(8) = 48 V = 48(15) V = 720 units3

  9. Find the volume. Break it into smaller parts. Vtop = 10(2)(5) = 100 Vbottom= 7(10)(4) = 280 Total Volume = 100 + 280 = 380 units3

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