Lesson 11

Squares and Cubes

Let’s investigate perfect squares and perfect cubes.

Problem 1

What is the volume of this cube?

cube, side length = 2 centimeters

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?

    Net of a triangular prism 

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

(From Unit 1, Lesson 11.)

Problem 7

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

trianglular prism with dimensions provided
(From Unit 1, Lesson 12.)