Lesson 11

Slicing Solids

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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

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.
Two figures, a triangle and a trapezoid.

 

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.

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 7, Lesson 2.)

Problem 5

Two months ago, the price, in dollars, of a cell phone was \(c\).

  1. Last month, the price of the phone increased by 10%. Write an expression for the price of the phone last month.
  2. This month, the price of the phone decreased by 10%. Write an expression for the price of the phone this month.
  3. Is the price of the phone this month the same as it was two months ago? Explain your reasoning.

Solution

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(From Unit 4, Lesson 8.)