Lesson 18Surface Area of a Cube

Learning Goal

Let’s write a formula to find the surface area of a cube.

Learning Targets

I can write and explain the formula for the surface area of a cube.
When I know the edge length of a cube, I can find its surface area and express it using appropriate units.

Lesson Terms

cubed
exponent
squared

Warm Up: Exponent Review

Select the greater expression of each pair without calculating the value of each expression. Be prepared to explain your choices.

1. $10 \cdot 3$
2. $10^{3}$
1. $13^{2}$
2. $12 \cdot 12$
1. $97 + 97 + 97 + 97 + 97 + 97$
2. $5 \cdot 97$

Activity 1: The Net of a Cube

Problem 1

A cube has edge length 5 inches.

Draw a net for this cube, and label its sides with measurements.
What is the shape of each face?
What is the area of each face?
What is the surface area of this cube?
What is the volume of this cube?

Problem 2

A second cube has edge length 17 units.

Draw a net for this cube, and label its sides with measurements.
Explain why the area of each face of this cube is $17^{2}$ square units.
Write an expression for the surface area, in square units.
Write an expression for the volume, in cubic units.

Activity 2: Every Cube in the Whole World

A cube has edge length $s$ .

Draw a net for the cube.
Write an expression for the area of each face. Label each face with its area.
Write an expression for the surface area.
Write an expression for the volume.

Lesson Summary

The volume of a cube with edge length $s$ is $s^{3}$ .

A 5 by 5 by 5 cube.

A cube has 6 faces that are all identical squares. The surface area of a cube with edge length $s$ is $6 \cdot s^{2}$ .

A net for a cube with each square labeled $s^2$.