Math Problem Statement

isolate r

Isolate r from the equation A = πr^2.

Solution

The equation in the image is:

A=πr2A = \pi r^2

To isolate rr, follow these steps:

  1. Divide both sides of the equation by π\pi: Aπ=r2\frac{A}{\pi} = r^2

  2. Take the square root of both sides to solve for rr: r=Aπr = \sqrt{\frac{A}{\pi}}

Thus, r=Aπr = \sqrt{\frac{A}{\pi}} is the expression for rr in terms of AA.

Would you like more details or have any questions?

Here are 5 related questions:

  1. What is the radius if the area AA is 100 square units?
  2. How does changing the area AA affect the radius rr?
  3. What is the area if the radius rr is 5 units?
  4. Can you express the diameter dd in terms of the area AA?
  5. What happens to the radius if the area is quadrupled?

Tip: When solving equations involving powers, always consider whether you need to take the square root, cube root, etc., to isolate variables.

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Math Problem Analysis

Mathematical Concepts

Algebra
Geometry

Formulas

A = πr^2
r = √(A/π)

Theorems

Area of a Circle

Suitable Grade Level

Grades 7-9