Lesson 10 Measure Figures Made From Prisms

- Let’s find the volume of more figures.

Warm-up Number Talk: Times Ten

Arched entryway and a bookshelf.

Find the value of each expression mentally.

$6 \times 2$
$6 \times 2 \times 10$
$6 \times 20 \times 10$
$60 \times 20 \times 10$

Activity 1 Find the Volume of Figures

Problem 1

6-sided rectangular prism.

How can we find the missing side lengths?

Problem 2

6-sided rectangular prism.

Partner A: Find the volume of Figure 1.

Partner B: Find the volume of Figure 2.

8-sided figure. — Figure 1

8-sided figure. — Figure 2

Activity 2 Expressions for the Volume of Figures

Problem 1

Figure composed of two rectangular prisms.

Explain how each expression represents the volume of the figure. Show your thinking. Organize it so it can be followed by others.

$((2 \times 3) \times 4) + ((3 \times 3) \times 2)$
$(5 \times 6) + (3 \times 4)$

Problem 2

8-sided figure.

How does each expression represent the volume of the prism? Explain or show your thinking. Organize it so it can be followed by others.

$(5 \times 8 \times 6) + (5 \times 4 \times 9)$ cubic inches
$(5 \times 4 \times 3) + (5 \times 12 \times 6)$ cubic inches

Practice Problem

Problem 1

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

6-sided rectangular prism.