If the lengths of the radii of two circles are 1 and 4 respectively, what is the ratio of their circumference and of their areas?

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eninsala06 · Accepted Answer

Circumference of a circle based on its radius  Cr=2πr  The circumference of a circle is in direct proportion to the radius.   So two circles with radii in the ratio 1:4 will have circumferences in the ratio 1:4  Area of a circle based on its radius  Ar=πr2  The area of a circle is in direct proportion to the square of its radius.  So two circles with radii in the ration 1:4 will have areas in the ratio 1:16

vrangett · Accepted Answer

Although the answers below all work, there is an easy, faster shortcut   If two objects are similar, their areas and side lengths have a special relationship, specifically, A∞r2  Since all circles are similar, we can apply this property to the problem  A∞r2  A4A=(RxR)2  14=1x  12=1x  x=2  So it is a 1 to 2 ratio

alenahelenash · Accepted Answer

If the ratio of the area of two circles is 1:4, then what is the ratio of their circumferences? The areas are (π)r2/(π)R2 or r2/R2=14=(12)2. So their circumferences will be in the ratio of 1:2

If the lengths of the radii of two circles are

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