What is the circumference of a 15-inch circle if the diameter of a circle is directly proportional to its radius and a circle with a 2-inch diameter has a circumference of approximately 6.28 inches?

1 Answer
Meave60
Dec 30, 2014

I believe the first part of the question was supposed to say that the circumference of a circle is directly proportional to its diameter. That relationship is how we get #pi#. We know the diameter and the circumference of the smaller circle, #"2 in"# and #"6.28 in"# respectively. In order to determine the proportion between the circumference and diameter, we divide the circumference by the diameter, #"6.28 in"/"2 in"# = #"3.14"#, which looks a lot like #pi#. Now that we know the proportion, we can multiply the diameter of the larger circle times the proportion to calculate the circumference of the circle. #"15 in"# x #"3.14"# = #"47.1 in"#.

This corresponds to the formulas for determining the circumference of a circle, which are #C# = #pi##d# and #2##pi##r#, in which C is circumference, d is diameter, r is radius, and #pi# is pi .

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