More Nets, More Surface Area

Warmup

Activity #1

Create Your Own NET.

You are going to watch a video now on how to create a Net. Follow the steps to find the Surface Area of common examples of polyhedra. You may want to write down the steps to guide you. Remember that you can also come back to the video for reference.

• Click on Play to continue whenever the video pauses to explain a step.

• Now is your turn to use the applet below to create your own net. Take note that you can change the view of the 3-D plane through any angle.

• When you are done creating your own net, use the same applet to find the Surface area of the following polyhedra;

(1.) A cube of sides 2 cm. (Hint; Your 2D polygon should be a square of sides 2 cm.)

(2.) A prism with a square base of sides 2 cm, and the height is 3 cm.

(3.) A prism with a rectangular base of sides 3 cm by 2 cm, and the height is 4 cm.

Activity #2

Practice Drawing a NET.

Polyhedral nets are a useful aid to the study of polyhedra and solid geometry in general, as they allow for physical models of polyhedra to be constructed from material such as thin cardboard.

• Use the graph paper below to practice drawing the net of each one of the following polyhedra;
• Use the side length of a square as 1 unit.
• Label each polygon on a net with a name or number.

• Find the surface area of each polyhedron above. (You can illustrate your thinking in the applet.)

Activity #3

Compare Surface Area of NET Structures.

Here below are the nets of three cardboard boxes – all rectangular prisms. The boxes will be packed with 1-centimeter cubes. All lengths are in centimeters.

• Compare the surface areas of the boxes. 

(1.) Which box will use the least cardboard? Use on the applet to show your reasoning.

• Also compare the volumes of these boxes in cubic centimeters.

(2.) Which box will hold the most 1-centimeter cubes? Use on the applet to show your reasoning.

In the applet above, the picture at the bottom shows the net of a cube.

• Use the RIGID POLYGON tool in the applet below to draw a different net of a cube.
• Draw another one.  And then another one.

How many different nets can be drawn and assembled into a cube?

Challenge #1

Jada drew a net for a polyhedron and calculated its surface area.

(1.) What polyhedron can be assembled from this net?

(2.) Jada made some mistakes in her area calculation. What were the mistakes?

Challenge #2

Here are two polyhedra and their nets. Label all edges in the net with the correct lengths.

Challenge #3

Twelve cubes are stacked to make this figure.

(1.) What is its surface area?

(2.) How would the surface area change if the top two cubes are removed? Show your reasoning.