   SEARCH HOME Math Central Quandaries & Queries  Question from dennis, a student: I have this work that says how are the value of the ratios for the perimeters related to the scale factor? PLEASE HELP ME OUT Dennis,

Look at my response to Riley's similar question. In his problem we were considering rectangles so try a circle. Suppose you have a circle of radius 2 cm. Find its perimeter (circumference) and area. Now multiply by a scale factor, for example a scale factor of 3. The circle is then expanded to one with radius 2 × 3 = 6 cm. What is its perimeter and area? How do these relate to the perimeter and area of the smaller circle?

Now try it a little more abstractly. Suppose the scale factor is k. The circle of radius 2 cm is then scaled to a circle with radius 2k cm. What is its perimeter and area? How do these relate to the perimeter and area of the original circle?

Harley     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.