More Nets, More Surface Area

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To 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.

Use the applet below 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 arectangular base of sides 3 cm by 2 cm, and the height is 4 cm.

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Practice Drawing a NET.

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. You can illustrate your thinking in the app above.

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Comparing Surface Area of NET Structures.

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

(1). Compare the surface areas of the boxes. Which box will use the least cardboard? Show your reasoning.

(2). Now compare the volumes of these boxes in cubic centimeters. Which box will hold the most 1-centimeter cubes? Show your reasoning.

(3). Now compare the volumes of these boxes in cubic centimeters. Which box will hold the most 1-centimeter cubes? Show your reasoning.

(4). In the app above, the lower most picture shows the net of a cube. Use the RIGID POLYGON tool in the app 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?

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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?

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

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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.