A circle of radius r has area A, where A = πr². What is r in terms of A?
Understand the Problem
The question is asking to express the radius r of a circle in terms of its area A. It provides the area formula A = πr². We will solve for r to find the correct expression based on the given options.
Answer
$$ r = \sqrt{\frac{A}{\pi}} $$
Answer for screen readers
The expression for the radius $r$ in terms of the area $A$ is: $$ r = \sqrt{\frac{A}{\pi}} $$
Steps to Solve
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Start with the area formula The area $A$ of a circle is given by the formula: $$ A = \pi r^2 $$
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Isolate $r^2$ To express $r$ in terms of $A$, first isolate $r^2$: $$ r^2 = \frac{A}{\pi} $$
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Take the square root Next, take the square root of both sides to solve for $r$: $$ r = \sqrt{r^2} = \sqrt{\frac{A}{\pi}} $$
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Final expression for $r$ Thus, the expression for the radius $r$ in terms of the area $A$ is: $$ r = \frac{\sqrt{A}}{\sqrt{\pi}} $$
The expression for the radius $r$ in terms of the area $A$ is: $$ r = \sqrt{\frac{A}{\pi}} $$
More Information
This formula shows how the radius of a circle can be derived from its area. It emphasizes the relationship between the area and the radius, highlighting the role of π, a fundamental constant in circles.
Tips
- Confusing the formula for the area of a circle with that of other shapes.
- Forgetting to take the square root after isolating $r^2$.
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