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.

Dilate the circle in the interactive below the following table to assist in the completion of the table.

• Fill in the “Radius of Dilated Circle” column.
• Make sure the black dot in the upper left hand corner is next to “Show radius.”
• Create a circle with the original radius. Note the circumference in units.
• Create a circle with the dilated radius. Note the circumference.
• Fill in the last column of the table.

Interactive popup. Assistance may be required.

Click here to see a completed table

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	12.56 units	25.12 units	2
2 units	1.5	3 units	12.56 units	18.84 units	1.5
2 units	0.5	1 unit	12.56 units	6.28 units	0.5

Extra Dilations

Using the information from the table, fill in the last two rows.

Interactive popup. Assistance may be required.

Click here to see a completed table

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	12.56 units	25.12 units	2
2 units	1.5	3 units	12.56 units	18.84 units	1.5
2 units	0.5	1 unit	12.56 units	6.28 units	0.5
2.4 units	1.5	3.6 units	15.08 units	22.62 units	1.5
2.4 units	0.8	1.92 units	15.08 units	12.06 units	0.8

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?

Check Your Answer

The scale factor of the circumference is the same as the scale factor of the radii.

Practice