Math Problem Statement

Solve for the given variables:

a) A = 𝜋r2 , for r (don't put the plus or minus (±) here as the system will reject it )

    r = 

Solution

To solve for rr in the equation A=πr2A = \pi r^2, follow these steps:

  1. Start with the equation: A=πr2A = \pi r^2

  2. Divide both sides by π\pi to isolate r2r^2: Aπ=r2\frac{A}{\pi} = r^2

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

Thus, the solution for rr is: r=Aπr = \sqrt{\frac{A}{\pi}}

Would you like more details on this solution?

Here are some related questions:

  1. What is the value of rr if A=50A = 50 square units?
  2. How does the equation change if the shape is an ellipse instead of a circle?
  3. Can you express rr in terms of another variable related to circumference CC?
  4. What happens to rr if you double the area AA?
  5. How is this formula derived from the basic geometry of a circle?

Tip: Always double-check the units of AA to ensure correct application of the formula.

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Math Problem Analysis

Mathematical Concepts

Algebra
Geometry
Area of a Circle

Formulas

A = 𝜋r²
r = √(A/𝜋)

Theorems

Area of a Circle

Suitable Grade Level

Grades 7-9