# How Do 3D Printers Work?

### New York State Common Core Math Geometry, Module 3, Lesson 13

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

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

1. 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?
2. 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?
3. 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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