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Surface Area & Volume

Lesson 22. Surface Area & Volume. Volume of Composite Solids. Warm-Up. Write the volume formula for each solid. Square prism Rectangular prism Triangular pyramid Cylinder Cone Pentagonal pyramid. Volume of Composite Solids. Target: Calculate the volume of composite solids.

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Surface Area & Volume

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  1. Lesson 22 Surface Area & Volume Volume of Composite Solids

  2. Warm-Up Write the volume formula for each solid. • Square prism • Rectangular prism • Triangular pyramid • Cylinder • Cone • Pentagonal pyramid

  3. Volume of Composite Solids Target: Calculate the volume of composite solids.

  4. Vocabulary • Composite solid: A solid made of two or more three- dimensional geometric figures.

  5. Volume of Composite Solids • Identify the different types of solids in the figure. • Calculate the volume of each solid. • Find the sum of the volumes.

  6. Example 1 Find the volume of the composite solid. Use 3.14 for π. • This composite figure is made of a cylinder and a cone. • Write each formula. • Substitute known values. • Find the value of the power. • Multiply. • Find the sum of the volumes. V ≈ 50.24 + 12.56 = 62.8 • The volume of the solid is about 62.8 ft3.

  7. Example 2 Find the approximate remaining volume when a cylindrical hole is drilled out of the prism. Use 3.14 for . • This prism is made of a prism and with a cylinder removed. • Write the formulas needed. • Substitute known values. • Find the value of the power. • Multiply. • Find the difference of the volumes. V ≈ 512 – 100.48 ≈ 411.52 • The remaining volume is about 411.52 cm3.

  8. Exit Problem • Find the volume of the composite solid. Use 3.14 for .

  9. Communication Prompt • Draw a diagram of your own composite solid then explain how to find the volume of it. • Are there any shortcuts for finding the volume of composite solids?

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