Missing Radius From Area

Missing radius from area

When the area of a circle is known, the radius can be found by reversing the area formula.

1) Start with the circle area formula

a = \pi r^2

Here, the area is given and the radius is unknown.

2) Isolate the radius

1. Divide both sides by \pi.
2. Take the square root of both sides.

This gives

r = \sqrt{\frac{A}{\pi}}

where (A) is the given area.

3) Simplify the answer

• If the area is an exact multiple of (\pi), simplify the fraction before taking the square root.
• If the result is not a perfect square, leave the radical in simplest form.
• If a decimal is needed, use the square root value carefully and round only if instructed.

4) Check your work

Substitute your radius back into (A = \pi r^2). The result should match the original area.

Example check

If (A = 49\pi), then [ r = \sqrt{\frac{49\pi}{\pi}} = \sqrt{49} = 7. ] A quick substitution gives (\pi(7^2) = 49\pi), so the answer is correct.