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://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=AKIAXQCCIHWF3XOEFOW4%2F20240701%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240701T081812Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=29a1a4eb9e5d9b3fa933118a6929d16d129a8142347ff45a42c15a3caf6b072d)
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://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=AKIAXQCCIHWF3XOEFOW4%2F20240701%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240701T081812Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=eeaefce97b62b680da9d32b6a7c60a72d17b2d5f97e5c813bf8f5640fe1e06fb)
![Two figures, a triangle and a trapezoid.](https://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=AKIAXQCCIHWF3XOEFOW4%2F20240701%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240701T081812Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=b43b4ce93a490276999fc7c7ce94457a18eaad58562545079b504cde7f528ed7)
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://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=AKIAXQCCIHWF3XOEFOW4%2F20240701%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240701T081812Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=de72e533c699a1993c8fe0b6e18737ab1b752e1057e47070a88b1fc0fe584924)
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.)