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?

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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?

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Answer 1 · 2014-12-30T11:00:03

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 $π$ $pi$ . We know the diameter and the circumference of the smaller circle, $2 in$ $"2 in"$ and $6.28 in$ $"6.28 in"$ respectively. In order to determine the proportion between the circumference and diameter, we divide the circumference by the diameter, $\frac{6.28 in}{2 in}$ $"6.28 in"/"2 in"$ = $3.14$ $"3.14"$ , which looks a lot like $π$ $pi$ . 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. $15 in$ $"15 in"$ x $3.14$ $"3.14"$ = $47.1 in$ $"47.1 in"$ .

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

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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?

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