# ﻿Applying Circumference

Warmup

Activity #1

Apply Circumference to Solve Word Problems.

The field inside a running track is made up of a rectangle that is 84.39 m long and 73 m wide, together with a half-circle at each end.

• Study the diagram and answer the questions that follow.

(1.) What is the distance around the inside of the track? Explain or show your reasoning.

(2.) The track is 9.76 m wide all the way around. What is the distance around the outside of the track? Explain or show your reasoning.

(3.) This size running track is usually called a 400-meter track. However, if a person ran as close to the “inside” as possible on the track, they would run less than 400 meters in one lap. How far away from the inside border would someone have to run to make one lap equal exactly 400 meters?

Activity #2

Identify Components of a Circle in Word Problems.

• Identify each measurement in the problems below as the diameter, radius, or circumference of the circular object.

Activity #3

A bug was sitting on the tip of the propeller blade when the propeller started to rotate. The bug held on to the end of the rotation before flying away.

Apply Circumference in Solving Problems.

• Beginning with one revolution, click on the button to spin the propellers and enter the distance to the nearest whole number that the bug travels before flying off.
• Click on the button and click to add the number of revolutions.
• Click on and continue filling the table until you get to 6 revolutions. Assume pie to be 3.14. Do not enter your answer in the applet. Leave the blade length to the default, 18.

Challenge #1

Kiran bent some wire around a rectangle to make a picture frame. The rectangle is 8 inches by 10 inches.

(1). Find the perimeter of the wire picture frame. Explain or show your reasoning.

Challenge #2

Kiran bent some wire around a rectangle to make a picture frame. The rectangle is 8 inches by 10 inches.

(2). If the wire picture frame were stretched out to make one complete circle, what would its radius be?

Challenge #3

A half circle is joined to an equilateral triangle with side lengths of 12 units.

What is the perimeter of the resulting shape?

Quiz Time