### Dr. Sarah's Applications of Geometry and Geometric Thinking - Physical Models

1. Use the playdough to form a ball. Make a cylinder that is the same diameter and height as the diameter of your sphere. Smush the sphere onto the (inside) bottom of the cylinder. What fraction of the cylinder does the sphere take up?

2. What are the modeling issues that arose when you tried to make your sphere and cylinder?

3. Take the plastic cylinder and cone. How many cones of sand does it take to fill up the cylinder?

What fraction of the cylinder does the cone take up?

4. Use your answers in 1 and 3 to make (and write down) a conjecture relating the cylinder to the cone plus the sphere.

Test your conjecture by using the plastic models and sand and explain the results.

5. Take the cube and the square pyramid. How many square pyramids does it take to fill up the cube?

6. Given the 3 red Zometool pieces and 1 white connector, construct a model with four triangles. Draw a picture of your model.

7. Use the blue Zometool pieces and connectors to construct an icosahedron and a cube.

8. Take your models with you to the computer room. We'll come back together there. If you are waiting for us to do so, access the class website and begin working on the homework for next week (see other side of this sheet).