Lesson 12
Surface Area of a Cube
Let’s write a formula to find the surface area of a cube.
Problem 1
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What is the volume of a cube with edge length 8 in?
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What is the volume of a cube with edge length \(\frac 13\) cm?
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A cube has a volume of 8 ft3. What is its edge length?
Problem 2
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What three-dimensional figure can be assembled from this net?
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If each square has a side length of 61 cm, write an expression for the surface area and another for the volume of the figure.
Problem 3
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Draw a net for a cube with edge length \(x\) cm.
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What is the surface area of this cube?
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What is the volume of this cube?
Problem 4
Here is a net for a rectangular prism that was not drawn accurately.
![Net of rectangular prism](https://cms-im.s3.amazonaws.com/bUmunmyozsPNGJTzHpRjCfh6?response-content-disposition=inline%3B%20filename%3D%226-6.1.E.PP_Image_10.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.E.PP_Image_10.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T033844Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=6ac20e3bfd5b4803fbfe92e0c784a87f426d7f4ca6b5b2e028a5709c29acb184)
- Explain what is wrong with the net.
- Draw a net that can be assembled into a rectangular prism.
- Create another net for the same prism.
Problem 5
State whether each figure is a polyhedron. Explain how you know.
![Two figures, A and B. Figure A is a cylinder, figure B is a prism with 7 sided polygons as faces.](https://cms-im.s3.amazonaws.com/chNgvtLu2t4tGdWeBu3KmKs3?response-content-disposition=inline%3B%20filename%3D%226-6.1.E.PP.New.Image.16.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.E.PP.New.Image.16.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T033844Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=c1e007f01d2b90c01e56dba28f1085e1749581fe26b5cb5ee207e2ba025f1fe6)
Problem 6
Here is Elena’s work for finding the surface area of a rectangular prism that is 1 foot by 1 foot by 2 feet.
![rectangular prism with student's work to calculate surface area shown](https://cms-im.s3.amazonaws.com/K5iG4SMkoptuXzyZubLPBfMe?response-content-disposition=inline%3B%20filename%3D%226-6.1.E.PP.New.Image.06.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.E.PP.New.Image.06.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T033844Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=4b86b6962c6e80ba60344d5fd8ea63086e45f60a5b5b4dfee0624ff1683eb66d)
She concluded that the surface area of the prism is 296 square feet. Do you agree with her? Explain your reasoning.