If a circle has area 36π, what is the radius?

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Multiple Choice

If a circle has area 36π, what is the radius?

Explanation:
The circle area grows with the square of the radius, described by A = πr^2. Here the area is 36π, so set πr^2 = 36π. Divide both sides by π to get r^2 = 36, and use the nonnegative radius, giving r = 6. The other radii would yield areas that don’t match 36π (for example, r = 3 gives 9π, r = 9 gives 81π, etc.), so they don’t fit. Since radius is nonnegative in standard geometry, 6 is the correct radius.

The circle area grows with the square of the radius, described by A = πr^2. Here the area is 36π, so set πr^2 = 36π. Divide both sides by π to get r^2 = 36, and use the nonnegative radius, giving r = 6. The other radii would yield areas that don’t match 36π (for example, r = 3 gives 9π, r = 9 gives 81π, etc.), so they don’t fit. Since radius is nonnegative in standard geometry, 6 is the correct radius.

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