Which equation is equivalent to A = (π)r²?

The equation A = (π)r² describes the relationship between the area of a circle (A) and its radius (r), with π being a constant approximately equal to 3.14. To find an equivalent equation that isolates the variable r, we want to manipulate the original equation in such a way that r can be expressed in terms of A.

Starting with A = (π)r², we can rearrange this equation step by step:

1. Divide both sides by π to isolate r²:

r² = A/π

2. To solve for r, take the square root of both sides:

r = √(A/π)

When examining the given choices, option B, √(A/π) = r, aligns perfectly with this result. It clearly expresses r as the square root of A divided by π, effectively representing the same relationship depicted in the original equation.

Understanding this transformation is crucial, as it showcases how variables can be rearranged in mathematical equations while keeping their relationships intact. This skill is particularly useful in fields like engineering, where such transformations frequently arise in calculations and assessments.