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| Math Central | Quandaries & Queries |
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Question from Amanda, a parent: what is the area of a circle with a circumference of 3000 metres? |
Amanda,
The area of a circle is given by the formula A = π r2, where A is the area and r is the radius. The circumference of a circle is C = 2 π r.
If we "solve for r" in the second equation, we have r = C / (2 π ). Now we use this to replace r in the first equation: A = π [ C / (2 π ) ]2.
When we simplify this, we get A = C2 / (4 π).
Now you can put your value of C into this equation and find A. Remember, π is about 3.1416.
Stephen La Rocque.
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