Finding The Area Of A Circle From Its Circumference - Math Central

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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.

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.