# Lesson 17

Squares and Cubes

Let’s investigate perfect squares and perfect cubes.

### Problem 1

What is the volume of this cube?

### Problem 2

1. Decide if each number on the list is a perfect square.

16

20

25

100

125

144

225

10,000

2. Write a sentence that explains your reasoning.

### Problem 3

1. Decide if each number on the list is a perfect cube.

1

3

8

9

27

64

100

125

2. Explain what a perfect cube is.

### Problem 4

1. A square has side length 4 cm. What is its area?

2. The area of a square is 49 m2. What is its side length?

3. A cube has edge length 3 in. What is its volume?

### Problem 5

Prism A and Prism B are rectangular prisms.

• Prism A is 3 inches by 2 inches by 1 inch.
• Prism B is 1 inch by 1 inch by 6 inches.

Select all statements that are true about the two prisms.

A:

They have the same volume.

B:

They have the same number of faces.

C:

More inch cubes can be packed into Prism A than into Prism B.

D:

The two prisms have the same surface area.

E:

The surface area of Prism B is greater than that of Prism A.

(From Unit 1, Lesson 16.)

### Problem 6

1. What polyhedron can be assembled from this net?

2. What information would you need to find its surface area? Be specific, and label the diagram as needed.

(From Unit 1, Lesson 14.)

### Problem 7

Find the surface area of this triangular prism. All measurements are in meters.

(From Unit 1, Lesson 15.)