# Lesson 11

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 12.)

### Problem 6

1. What polyhedron can be assembled from this net?