Section C: Practice Problems Volume of Solid Figures

Section Summary

Details

Some figures are made from two rectangular prisms. We can decompose these figures and find the volume of each prism. Then, we add the volumes of the two prisms to find the total volume of the figure.

There is often more than one way to decompose figures made from 2 rectangular prisms. These expressions can be used to find the volume of the figure:
$(3 \times 3 \times 5) + (5 \times 2 \times 5)$
$(3 \times 5 \times 5) + (2 \times 2 \times 5)$

Problem 1 (Lesson 9)

What is the volume of this figure? Explain or show your reasoning.

Rectangular prism with additional cubes attached to front.

Problem 2 (Lesson 10)

Find the volume of the figure. Explain or show your reasoning.

Problem 3 (Lesson 11)

Find the volume of the figure. Explain or show your reasoning.

Two rectangular prisms, one in front of the other.

Problem 4 (Lesson 12)

This is a diagram of a bedroom. What is the volume of the bedroom? Explain or show your reasoning.

Problem 5 (Exploration)

Han says that the volume of this rectangular prism is 50 times as great as a 2-inch cube. Do you agree with Han? Explain or show your reasoning.
Han says that he can fit 50 2-inch cubes in this rectangular prism. Do you agree with Han? Explain or show your reasoning.

Problem 6 (Exploration)

Two common sizes of shipping boxes are 5 inches by 6 inches by 15 inches and 11 inches by 6 inches by 15 inches. Which size box would you choose to ship the student workbooks for your math class? Explain or show your reasoning.