In terms of pi it is 1/3π or just 1/3π feet. If 3.1415 is assumed for pi, then the answer is 0.31831927 feet approximately.
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You should clarify whether "1-foot circle" refers to a circle with a radius of 1 foot, a diameter of 1 foot, or a circumference of 1 foot. The circumference of a circle is equal to the diameter times pi (approximately 3.14).
To find the area of a circle, either the diameter or the circumference must be known. The formula for the area from the diameter is (pi)*(1/2 of diameter) squared. From the circumference, simply substitute (circumference / pi) for diameter.
The circumference of a circle if the diameter is 1 equals 3.1412 (π).
The circumference of a circle with a diameter of 1 is Pi: 3.1416
If a circle has a circumference of 3.14 (pi) the diameter is: 1