Lesson 11: Slicing Solids
Let’s see what shapes you get when you slice a three-dimensional object.
Illustrative Math Unit 7.7, Lesson 11 (printable worksheets)
Lesson 11 Summary
The following diagrams show how a cross section is formed when we slice through a three-dimensional figure.
Lesson 11.1 Prisms, Pyramids, and Polyhedra
Describe each shape as precisely as you can. Click on the applet and drag the mouse to show the object turning in 3D.
Lesson 11.2 What’s the Cross Section?
Here are a rectangular prism and a pyramid with the same base and same height. Drag the large red point up and down to move the plane through the solids.
- If we slice each solid parallel to its base halfway up, what shape cross sections would we get? What is the same about the cross sections? What is different?
- If we slice each solid parallel to its base near the top, what shape cross sections would we get? What is the same about the cross sections? What is different?
Are you ready for more?
Describe the cross sections that would result from slicing each solid perpendicular to its base.
Lesson 11.3 Card Sort: Cross Sections
Your teacher will give you a set of cards. Sort the images into groups that make sense to you. Be prepared to explain your reasoning.
Lesson 11.4 Drawing Cross Sections
Use the applet to draw each cross section and describe it in words.
- Here is an applet with a rectangular prism, 4 units by 2 units by 3 units.
a. A plane cuts the prism parallel to the bottom and top faces.
b. The plane moves up and cuts the prism at a different height.
c. A vertical plane cuts the prism diagonally.
- A square pyramid has a base that is 4 units by 4 units. Its height is also 4 units.
a. A plane cuts the pyramid parallel to the base.
b. A vertical plane cuts the prism.
- A cube has an edge of length 4.
a. A plane cuts off the corner of the cube.
b. The plane moves farther from the corner and makes a cut through the middle of the cube.
Lesson 11 Practice Problems
- 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?
- Describe how to slice the three-dimensional figure to result in each cross section.
- Here are two three-dimensional figures.
Describe a way to slice one of the figures so that the cross section is a rectangle.
- Each row contains the degree measures of two supplementary angles. Complete the table.
- Two months ago, the price, in dollars, of a cell phone was c.
a. Last month, the price of the phone increased by 10%. Write an expression for the price of the phone last month.
b. This month, the price of the phone decreased by 10%. Write an expression for the price of the phone this month.
c. Is the price of the phone this month the same as it was two months ago? Explain your reasoning.
The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.
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