Lesson 12
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?
Solution
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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.
Solution
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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?
Solution
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Problem 4
Here is a net for a rectangular prism that was not drawn accurately.
![Net of rectangular prism](https://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T102623Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=8177d869fd5f75afd6f59beaa716233a692f6c2e263900f5bbfb243f01c177de)
- 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.
Solution
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(From Unit 1, Lesson 11.)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://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T102623Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=a3daee6fa6d39167bddadd3bff7bc7de54e894eb855c6074147370d7a2f2c8f9)
Solution
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(From Unit 1, Lesson 11.)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://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T102623Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=811fdada4bc4ac31f9274618e5c02a91092375ab64b2cfe080c68bbd7bfda67e)
She concluded that the surface area of the prism is 296 square feet. Do you agree with her? Explain your reasoning.
Solution
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(From Unit 1, Lesson 10.)