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Lesson Plans and Worksheets for Geometry

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More Lessons for Geometry

Common Core For Geometry

Worksheets for Geometry, Module 3, Lesson 13

Student Outcomes

- Visualize cross-sections of three-dimensional objects.
- Have an understanding of how a 3D printer works and its relation to Cavalieri’s principle.

**How Do 3D Printers Work?**

Classwork

**Opening Exercise**

a. Observe the following right circular cone. The base of the cone lies in plane 𝑆, and planes 𝑃, 𝑄, and 𝑅 are all
parallel to 𝑆. Plane 𝑃 contains the vertex of the cone.

b. What happens to the cross-sections as we look at them starting with 𝑃′ and work toward 𝑆′?

**Exercise 1**

- Sketch five evenly spaced, horizontal cross-sections made with the following figure.

**Example**

Let us now try drawing cross-sections of an everyday object, such as a coffee cup.

**Exercises 2–4**

- A cone with a radius of 5 cm and height of 8 cm is to be printed from a 3D printer. The medium that the printer will use to print (i.e., the “ink” of this 3D printer) is a type of plastic that comes in coils of tubing that has a radius of 1 1/3 cm. What length of tubing is needed to complete the printing of this cone?
- A cylindrical dessert 8 cm in diameter is to be created using a type of 3D printer specially designed for gourmet kitchens. The printer will “pipe” or, in other words, “print out” the delicious filling of the dessert as a solid cylinder. Each dessert requires 300 cm3 of filling. Approximately how many layers does each dessert have if each layer is 3 mm thick?
- The image shown to the right is of a fine tube that is printed from a 3D printer that prints replacement parts. If each layer is 2 mm thick, and the printer prints at a rate of roughly 1 layer in 3 seconds, how many minutes will it take to print the tube?

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