# Modeling with Geometry Problems

## Geometry Quiz

Modeling with geometry problems test students in the following critical areas:

- application of geometric concepts in modeling situations

- use of geometric shapes, their measures, and their properties to describe objects

- application of concepts of density based on area and volume in modeling situations

Question 1: The 3-point line distance from the basket of a NBA basketball court is r = OC and d = OE in the corner. Which of the following is an expression of the value of angle ∠COD?

Question 2: Three identical cylinders are held next to each other with a rubber band. What is the length of the rubber band in its extended position over the three cylinders, as a function of radius of the cylinders, r?

Question 3: The paper clip in the figure below is made of steel wire. Calculate the length of steel wire required to make a paper clip and round to the nearest mm.

Question 4: An ice cream cone can be modeled by a semi sphere on top of a cone, as shown in the picture below. Calculate the volume of the ice cream cone as a function of r, if the height of the cone is h = 4r.

Question 5: The distance between New York and Los Angeles in a direct path along the Earth's surface is 2,400 miles. Assuming the Earth is a sphere with a radius of 4,000 miles, what is the angle between the radii in the figure below?

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