Surface Area of a Cube

Warmup

Activity #1

 Find the Surface Area of a Cube from the Net.

In the following activity, you are going to find the surface area of a cube from the net structure. Follow the instructions below.

• Take a few minutes to interact with the rectangular prism shown here below. ​
• Move the CREATE NET slider to create the net.
• Use the nets to find the surface area of the cube. The OPTIONS slider helps you to sort corresponding faces of the structure.

• Answer the following questions about the rectangular prism:

• Create a prism that has a length = 6 units, width = 6 units, and height = 6 units. ​
• Move the CREATE NET slider to create the net.
• Use the nets to find the surface area of the cube.

Activity #2

Find a Relation Between Side length and Surface Area of a cube.

The surface area of a cube is related to the side lengths. Find out how they are related in this activity. The original cube has side lengths 1 unit, follow the instructions below and complete the table that follows.

• Move the slider through a = 0.5, a = 1, a = 2, a = 3.
• Observe the net of the cube as you move through the different values.

• Complete the table below for the side length and Surface Area of the cube. if your answer is not a whole number, write it down as a decimal.

Did you expect the surface area of the box to be halved when the value of a is halved? Why or why not?

Activity #3

Draw the Net of a Cube When a Side Length is Given.

In this activity, you are going to draw the net of a cube when the side is given. Remember that all the side lengths of a cube are equal.

• A cube has edge length 5 inches. Draw a net for this cube, and label its sides with measurements.

• Answer the questions below.

(1.) What is the shape of each face?

(2.) What is the area of each face?

(3.) What is the surface area of this cube?

(4.) What is the volume of this cube?

• A second cube has edge length 17 units. Draw a net for this cube, and label its sides with measurements.

• Answer the questions below.

(1.) Explain why the area of each face of this cube is 17² square units.

(2.) Write an expression for the surface area, in square units.

(3.) Write an expression for the volume, in cubic units.

Quiz Time

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