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.
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.
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 |
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2 units | 0.5 |
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2.4 units | 1.5 |
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2.4 units | 0.8 |
Interactive popup. Assistance may be required.
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. The scale factor of the circumference is the same as the scale factor of the radii.