Lesson 17
Squares and Cubes
Let’s investigate perfect squares and perfect cubes.
Problem 1
What is the volume of this cube?
Problem 2

Decide if each number on the list is a perfect square.
16
20
25
100
125
144
225
10,000
 Write a sentence that explains your reasoning.
Problem 3

Decide if each number on the list is a perfect cube.
1
3
8
9
27
64
100
125
 Explain what a perfect cube is.
Problem 4

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

The area of a square is 49 m^{2}. What is its side length?

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.
They have the same volume.
They have the same number of faces.
More inch cubes can be packed into Prism A than into Prism B.
The two prisms have the same surface area.
The surface area of Prism B is greater than that of Prism A.
Problem 6

What polyhedron can be assembled from this net?

What information would you need to find its surface area? Be specific, and label the diagram as needed.
Problem 7
Find the surface area of this triangular prism. All measurements are in meters.