Question 695027: 1.) The area of a circle is 201 cm. Which is the circumference of the circle.
Answer by RedemptiveMath(80)   (Show Source):
You can put this solution on YOUR website! Analyzing this problem, we are given two different properties of a circle: area and circumference. Since we are dealing with both, it would be imperative to know what both formulas are. Area of a circle equals pi times radius squared. Circumference equals diameter times pi or twice the radius times pi. We can now notice the common link between the two properties: the radius. It would be essential to know what the radius is. Where do we start? Let us start with the property that already has an answer.
The way I am going to answer the next few parts may be different than what your teacher expects. Some teachers want the "exact" value of properties when we deal with π. Since π is irrational (i.e. non-terminating decimal that isn't classified as repeating), we cannot give an exact answer if we use 3.14 or 22/7 for it. (These are common approximations.) That is why some teachers leave the pi symbol in the answer. This lets us know that the answer is something times pi. This method has an answer that represents all of pi, which is given with the symbol π. For example, 14π is the exact form of 43.96 (14 times 3.14). I am going to answer everything in decimal notation (using 3.14 for π). If your teacher expects exact answers, then don't use any approximation for π and leave the symbol in the answer.
Area = πr^2. Our area is 201 cm^2, so
201 cm^2 = πr^2
201 cm^2 = 3.14(r^2)
64.01274 cm^2 = r^2
8.000796 cm ≈ r
r ≈ 8.000796 cm or 8 cm.
Since we know the radius r to be about 8 cm, we can solve for circumference by using the formula C = 2πr:
C = 2πr
C = 2rπ
C = 2(8)π
C = 16π
C ≈ 50.24 cm.
Your answer may vary depending on how many decimal places you used for pi and/or how far you rounded to. The exact answer for the radius would be (√201π)/(π) cm. The exact answer for the circumference would be 2(√201π) cm.
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