How do you convert π and r in the equation A = (π)r²?

How do you convert π and r in the equation A = (π)r²?

• A. 1 = A(π)r²
• B. √(A) = (π)r
• C. √(A/π) = r
• D. (A/π)² = r

Answer: (C)

In the equation A = πr², the area A of a circle is expressed in terms of its radius r. To isolate r, it is necessary to manipulate the equation systematically. Starting from the original equation, you can divide both sides by π to isolate r². This gives you the equation: r² = A/π. To find r, you then take the square root of both sides. This leads to the expression: r = √(A/π). This is why the choice that indicates the square root of (A/π) equals r is the correct one. The other choices do not accurately reflect proper algebraic manipulation of the equation. Choice A suggests a misconstrued rearrangement that does not provide useful information about the radius. Choice B implies a relationship between A, π, and r that does not truthfully represent the formula for the area of a circle. Choice D incorrectly suggests a squared relation that does not follow from the original area formula.

In the equation A = πr², the area A of a circle is expressed in terms of its radius r. To isolate r, it is necessary to manipulate the equation systematically.

Starting from the original equation, you can divide both sides by π to isolate r². This gives you the equation:

r² = A/π.

To find r, you then take the square root of both sides. This leads to the expression:

r = √(A/π).

This is why the choice that indicates the square root of (A/π) equals r is the correct one.

The other choices do not accurately reflect proper algebraic manipulation of the equation. Choice A suggests a misconstrued rearrangement that does not provide useful information about the radius. Choice B implies a relationship between A, π, and r that does not truthfully represent the formula for the area of a circle. Choice D incorrectly suggests a squared relation that does not follow from the original area formula.