If A = (π) r², then what is the radius r?

If A = (π) r², then what is the radius r?

• A. √(A x π)
• B. (A / π)²
• C. (A x π)²
• D. √(A / π)

Answer: (D)

To derive the radius from the area formula \( A = \pi r^2 \), you need to isolate \( r \). Start by dividing both sides of the equation by \( \pi \), which gives you: \[ \frac{A}{\pi} = r^2. \] Then, to find \( r \), take the square root of both sides: \[ r = \sqrt{\frac{A}{\pi}}. \] This is the mathematical process to find the radius when given the area \( A \). The correct choice matches this derived formula, which is \( \sqrt{\frac{A}{\pi}} \). By recognizing the steps in manipulating the area formula, you can accurately understand why this option represents the radius. The other choices do not accurately represent the mathematical manipulation necessary to isolate \( r \) based on the original area formula. They either involve incorrect operations or rearrangements that do not lead to solving for \( r \) in terms of \( A \) and \( \pi \). This reinforces the importance of careful algebraic manipulation when working with formulas in engineering contexts.

To derive the radius from the area formula ( A = \pi r^2 ), you need to isolate ( r ). Start by dividing both sides of the equation by ( \pi ), which gives you:

[ \frac{A}{\pi} = r^2. ]

Then, to find ( r ), take the square root of both sides:

[ r = \sqrt{\frac{A}{\pi}}. ]

This is the mathematical process to find the radius when given the area ( A ).

The correct choice matches this derived formula, which is ( \sqrt{\frac{A}{\pi}} ). By recognizing the steps in manipulating the area formula, you can accurately understand why this option represents the radius.

The other choices do not accurately represent the mathematical manipulation necessary to isolate ( r ) based on the original area formula. They either involve incorrect operations or rearrangements that do not lead to solving for ( r ) in terms of ( A ) and ( \pi ). This reinforces the importance of careful algebraic manipulation when working with formulas in engineering contexts.