Sam's mom has asked him to order pizza for dinner. When he calls his family's favorite pizza restaurant, the clerk asks him what size pizza he wants—10 inch, 14 inch, or 16 inch. Sam knows that three people will be eating the pizza—his mom, his dad, and himself. But he's never ordered pizza before, and he's not absolutely sure what those numbers mean. What size should he order, and will it be enough for his family?
Pizzas are almost always created as round pies, or circles. What part of a circle is the clerk describing when she tells Sam his choices?
The clerk is describing the diameter of the circle formed by the pizza—the distance from one side of the circle to the other. In geometry, diameter is defined more precisely, of course. It's a line segment that goes through the center of a circle and has endpoints on the circle.
Sam may need to ask a few more questions to figure out what size pie he should order, such as how many slices are in each pizza. Once he knows how the pie is cut, does Sam have enough information to visualize the amount of food?
If Sam knows how to figure the radius of a circle, he can more easily imagine the size of the slices. To be absolutely sure of each slice's size, though, Sam would need to find the area of the pizza and of each slice. In situations like ordering pizza, where making mistakes is not a serious problem, knowing the pie's diameter and the number of slices is enough to choose the right size to purchase.
Question
What kinds of situations would require you be very precise in your understanding of a circle's parts?
