Now that you have investigated with one type of polygon (rectangles), let's see if the relationship between the scale factor of a dilated polygon and the perimeter holds true for circles as well.

Recall that the perimeter of a circle is called the circumference.

This activity might not be viewable on your mobile device. Interactive exercise. Assistance may be required. Use the interactive sketch below to dilate Circle A using the ScaleFactor slider. Notice how the dilated circumference changes as you manipulate the figures in the interactive. You may also adjust the radius of Circle A by clicking and dragging Point B until the radius value changes to the desired number. Use this interactive sketch to complete the table beneath the sketch.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com
Radius of Original Circle
Scale
Factor of
Radii
Radius of Dilated Circle
Original Circumference
Dilated Circumference
Scale Factor of Circumference
2 units
2
4 units
12.57 units
25.13 units
2
2 units
1.5
2 units
0.5
2.4 units
1.5
2.4 units
0.8

Interactive popup. Assistance may be required.

Click here to see a completed table

Close Pop Up

What relationship do you see between the scale factor of the circumference and the scale factor of the radii for each of the 5 pairs of circles you constructed?

Interactive popup. Assistance may be required.

Check Your Answer

The scale factor of the circumference is the same as the scale factor of the radii. Close Pop Up

Practice

Interactive exercise. Assistance may be required.