Circle Applications

PAGE CONTENTS

Cartoon Teardrop

Gooey Pizza

Bug Jar

Link to Google doc

#1 Cartoon Teardrop

Goal: Find the circumference of arcs to compare two distances.

Two semicircular arcs, of radius 3 m and 5 m, are centered on the diameter of the larger semicircle as shown.

Which route from A to B is shorter: along the large semicircle or along the two smaller semicircles that touch at point C?

Model Credit: need to find.

#2 Gooey Pizza

Goal: Find the area of an annulus to compare areas of a pizza.

Jamal and his little brother Terry decided to cook a 9 inch pizza and share it 50-50. Terry likes the outer edge of the pizza (this includes the crust) and Jamal likes the gooey center part. Jamal decides to cut the pizza into the shape of an annulus. The length across the inside of the gooey center of the circle is 6.5 inches. Did Jamal divide the circle in half? if not, who got more pizza and how much more?

Model Credit: Crystal Pepsi: my favorite food

#3 Bug Jar Race

Goal: Find the distance of a race in a jar and compare it to distance in a larger jar.

Problem Statement

Jamal and Terry have circular bug jars of different dimensions. The boys each capture one bug and watch them run around the circular base of the bug jars. Jamal challenges Terry to a bug race, but he needs to determine a distance for the race in each of the respective jars that would be fair to both bugs. Jamal’s bug jar has a diameter of 18 cm. Terry’s bug jar has a diameter of 12 cm. Jamal decides that it would be best if the bugs run one complete turn in Terry’s smaller jar.

How many centimeters long is the race?

What is the arc measure of the racetrack in Jamal’s bug jar?

Graphic: 3D-Warehouse