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Calculating Volumes of Prisms and Cylinders: A Comprehensive Guide

This educational resource focuses on finding the volumes of various geometric solids, including prisms and cylinders. It provides examples for calculating the volume of rectangular prisms (e.g., 385 cubic inches) and triangular prisms (e.g., 270 cubic feet), along with detailed explanations on how to approach each problem. The guide also covers the volume of composite solids, illustrating the combined volumes from a rectangular prism and a cylindrical hole. Key concepts and vocabulary are outlined, making it ideal for students learning geometry.

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Calculating Volumes of Prisms and Cylinders: A Comprehensive Guide

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  1. Splash Screen

  2. Find the volumes of prisms and cylinders. • volume • cylinder • composite solid Main Idea/Vocabulary

  3. KC

  4. Find the Volumes of Prisms Find the volume of the rectangular prism. Volume of a prism Simplify. Answer: The volume is 385 cubic inches. Example 1

  5. A B C D Find the volume of the rectangular prism. A. 90 in3 B. 120 in3 C. 126 in3 D. 148 in3 Example 1

  6. The base is a triangle, so B = Find the Volumes of Prisms Find the volume of the triangular prism. Volume of a prism The height of the prism is 4. Simplify. Answer: The volume is 270 cubic feet. Example 2

  7. A B C D Find the volume of the triangular prism. A. 22 ft3 B. 30 ft3 C. 37 ft3 D. 45 ft3 Example 2

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  9. Find the Volume of a Cylinder Find the volume of the cylinder. Round to the nearest tenth. Volume of a cylinder Replace r with 3 and h with 12. V≈ 339.3 Simplify. Answer: The volume is about 339.3 cubic centimeters. Example 3

  10. A B C D Find the volume of the cylinder. Round to the nearest tenth. A. 140.1 in3 B. 152.5 in3 C. 169.6 in3 D. 183.4 in3 Example 3

  11. Find the Volume of a Composite Solid TOYS A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth. The block is a rectangular prism with a cylindrical hole. To find the volume of the block, subtract the volume of the cylinder from the volume of the prism. Example 4

  12. ≈ Find the Volume of a Composite Solid Rectangular Prism Cylinder Answer: The volume of the box is about 72 – 9.42 or 62.58 cubic centimeters. Example 4

  13. A B C D HOBBIES A small wooden cube has been glued to a larger wooden block for a whittling project. What is the volume of the wood to be whittled? A. 98 in3 B. 104 in3 C. 112 in3 D. 115 in3 Example 4

  14. End of the Lesson End of the Lesson

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