# Section A: Practice Problems Unit Cubes and Volume

## Section Summary

Details

We call the amount of space an object takes up volume. This prism has a volume of 120 cubes.

To find the volume of any prism, we can find the number of cubes in one layer and multiply that number by the number of layers. We can describe this prism as having 6 layers of 20 cubes, 4 layers of 30 cubes, or 5 layers of 24 cubes. We can use all of these expressions to represent the volume of the prism:
,
,
,

## Problem 1 (Pre-Unit)

Here is a diagram of the floor in a room.

What is the area of the floor? Explain or show your reasoning.

## Problem 2 (Pre-Unit)

What are the missing side lengths? Explain or show your reasoning.

## Problem 3 (Pre-Unit)

Which of these units would you use to measure the length of a pencil? Select all that apply.

1. centimeter

2. meter

3. kilometer

4. inch

5. foot

6. yard

7. mile

## Problem 4 (Pre-Unit)

Find the area of the figure shown here. Explain or show your reasoning.

## Problem 5 (Lesson 1)

Which has greater volume? Explain or show your reasoning.

## Problem 6 (Lesson 2)

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

## Problem 7 (Lesson 3)

What is the volume of the rectangular prism? Explain or show your reasoning.

## Problem 8 (Lesson 4)

Find the volume of each rectangular prism. Explain or show your reasoning.

## Problem 9 (Exploration)

Find some objects around you and compare their volume.

1. List the objects.

2. Which has the least volume? Which has the greatest?

3. Pick two of your objects and compare their volume.

## Problem 10 (Exploration)

1. How many different rectangular prisms can you make with 18 cubes? Explain or show your reasoning.

2. How many different rectangular prisms can you make with 24 cubes? Explain or show your reasoning.

3. How do the side lengths of each prism compare to one another? What patterns do you notice? Is this pattern true for the rectangular prisms you can make with 36 cubes?