Lesson 11
Slicing Solids
Problem 1
A cube is cut into two pieces by a single slice that passes through points \(A\), \(B\), and \(C\). What shape is the cross section?
![A cube is indicated. Point A is located on the back, top right vertex, Point B is located on the front, top left vertex, and Point C is located on the front, bottom left vertex](https://staging-cms-im.s3.amazonaws.com/7a3HJuWgnzTbhQHwgUATtXdK?response-content-disposition=inline%3B%20filename%3D%227-7.6.C.PP.Image.02.png%22%3B%20filename%2A%3DUTF-8%27%277-7.6.C.PP.Image.02.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=20240703T075421Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=539aca7913c6a9726aed3378e377f6b16a737670cd9e6411b248e405c30283cb)
Solution
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Problem 2
Describe how to slice the three-dimensional figure to result in each cross section.
Three-dimensional figure:
Cross sections:
![A pyramid, the base of which is a triangle.](https://staging-cms-im.s3.amazonaws.com/yudAeQVTcUJ9fvJaNYpwVvLE?response-content-disposition=inline%3B%20filename%3D%227-7.7.newPP_Image_6ghi.png%22%3B%20filename%2A%3DUTF-8%27%277-7.7.newPP_Image_6ghi.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=20240703T075421Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=d11ced72d9a839f40895331febde2b96f3ff9569fe204f2261f056e8a4a79495)
![Two figures, a triangle and a trapezoid.](https://staging-cms-im.s3.amazonaws.com/BNYkWEpmyXcxhg15yG2v2NxQ?response-content-disposition=inline%3B%20filename%3D%227-7.7.newPP_Image_7jkl.png%22%3B%20filename%2A%3DUTF-8%27%277-7.7.newPP_Image_7jkl.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=20240703T075421Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=63571e60330d5d0fddc971ee1f3e8dc485d59422784697a20ab51dffd9bc9215)
Solution
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Problem 3
Here are two three-dimensional figures.
![Two three-dimensional figures. Figure A a triangular prism. Figure B is a triangular pyramid.](https://staging-cms-im.s3.amazonaws.com/y1QdBS1CE3t74VFx5t8p12Mz?response-content-disposition=inline%3B%20filename%3D%227-7.7.newPP_Image_4abc.png%22%3B%20filename%2A%3DUTF-8%27%277-7.7.newPP_Image_4abc.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=20240703T075421Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e21ac4cee28bd8f749de13e57bf7dd07112e5f7e9131fe9a4624ba8a7aa54cdd)
Describe a way to slice one of the figures so that the cross section is a rectangle.
Solution
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Problem 4
Each row contains the degree measures of two supplementary angles. Complete the table.
measure of an angle | measure of its supplement |
---|---|
\(80^\circ\) | |
\(25^\circ\) | |
\(119^\circ\) | |
\(x\) |
Solution
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(From Unit 1, Lesson 12.)