Lesson 16
Surface Area of Right Prisms
Problem 1
Edge lengths are given in units. Find the surface area of each prism in square units.
![Five prisms.](https://cms-im.s3.amazonaws.com/9vLdafcNcB24rAkVLWQDc1SV?response-content-disposition=inline%3B%20filename%3D%227-7.7.newPP.prismsABCDE09.png%22%3B%20filename%2A%3DUTF-8%27%277-7.7.newPP.prismsABCDE09.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T234642Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=546e35bdb256dbb8aefde4249e99f610dbbf2bd6206ba6b72772b6a677b28854)
Solution
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Problem 2
Here is the base of a prism.
![An 8-sided figure, all angles right, lengths, centimeters. From the first vertex, a segment extends 8 right, then 5 down, then 3 left, then 2 up, then 2 left, then 2 down, then 3 left, then 5 up.](https://cms-im.s3.amazonaws.com/KENNdq3qzE3XB9M1mn8fnmvp?response-content-disposition=inline%3B%20filename%3D%227-7.6.C3.Image.02.png%22%3B%20filename%2A%3DUTF-8%27%277-7.6.C3.Image.02.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T234642Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=f01b2de90f2a28e5ad073fd0e35e2bf756df43adca66f4ebbabc17fa672ed576)
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If the height of the prism is 5 cm, what is its surface area? What is its volume?
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If the height of the prism is 10 cm, what is its surface area? What is its volume?
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When the height doubled, what was the percent increase for the surface area? For the volume?
Solution
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Problem 3
Select all the situations where knowing the volume of an object would be more useful than knowing its surface area.
Determining the amount of paint needed to paint a barn.
Determining the monetary value of a piece of gold jewelry.
Filling an aquarium with buckets of water.
Deciding how much wrapping paper a gift will need.
Packing a box with watermelons for shipping.
Charging a company for ad space on your race car.
Measuring the amount of gasoline left in the tank of a tractor.
Solution
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Problem 4
Priya says, “No matter which way you slice this rectangular prism, the cross section will be a rectangle.” Mai says, “I’m not so sure.” Describe a slice that Mai might be thinking of.
![A rectangular prism.](https://cms-im.s3.amazonaws.com/eKZrz4GZwG9qdoZtL7AjLwJJ?response-content-disposition=inline%3B%20filename%3D%227-7.7.newPP_Image_8mno.png%22%3B%20filename%2A%3DUTF-8%27%277-7.7.newPP_Image_8mno.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T234642Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=71fb11d8114d2bc2a962882340c1b121d93516be36f4e1fe0bbc88eb7eed4dce)
Solution
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(From Unit 6, Lesson 11.)Problem 5
\(B\) is the intersection of line \(AC\) and line \(ED\). Find the measure of each of the angles.
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Angle \(ABF\)
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Angle \(ABD\)
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Angle \(EBC\)
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Angle \(FBC\)
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Angle \(DBG\)
![Two lines and two rays that intersect at point B creating 6 angles.](https://cms-im.s3.amazonaws.com/NY2HeqWfEtjiZPVJDfji5fws?response-content-disposition=inline%3B%20filename%3D%227-7.6.A.PP.Image.11.png%22%3B%20filename%2A%3DUTF-8%27%277-7.6.A.PP.Image.11.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T234642Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e8207ddee7a3b7b77b5fdc82bb235eaa407d97604db85a39df5c660b95167d86)
Solution
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(From Unit 3, Lesson 13.)Problem 6
Write each expression with fewer terms.
- \(12m-4m\)
- \(12m-5k+m\)
- \(9m+ k-(3m-2k)\)
Solution
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(From Unit 4, Lesson 9.)