Volume of Composite Solids

Lesson 22

Write the volume formula for each solid.

1. Square prism

2. Rectangular prism

3. Triangular pyramid

4. Cylinder

5. Cone

6. Pentagonal pyramid

Target: Calculate the volume of composite solids.

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

1. Identify the different types of solids in the figure.

2. Calculate the volume of each solid.

3. Find the sum of the volumes.

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.

hr 2V hr 2

3

1V

)4()2)(14.3(V 2

)4)(4)(14.3(V

24.50V

)3()2)(14.3(3

1V 2

)3)(4)(14.3(3

1V

56.12V

Find the approximate remaining volumewhen a cylindrical hole is drilled out ofthe 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.

BhV)8)(88(V

512V

hr 2V )8()2)(14.3(V 2

)8)(4)(14.3(V 48.100V

Find the volume of the composite solid. Use 3.14 for .

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?