
Find the radius of a circle with an area of 262m^2.  Round your answer to the nearest tenth.

The area \( A \) of a circle is given by the formula:

\[
A = \pi r^2
\]

Where:
- \( A \) is the area,
- \( r \) is the radius, and
- \( \pi \approx 3.1416 \).

We are given \( A = 262 \, \text{m}^2 \). To find the radius \( r \), we rearrange the formula to solve for \( r \):

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

Substituting the given area:

\[
r = \sqrt{\frac{262}{\pi}} = \sqrt{\frac{262}{3.1416}}
\]

Let's calculate that.

\[
r \approx \sqrt{83.392} \approx 9.13 \, \text{m}
\]

Rounding to the nearest tenth, the radius is:

\[
r \approx 9.1 \, \text{m}
\]

Would you like more details or have any questions?

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Here are 5 related questions:
1. How would the radius change if the area doubled?
2. What is the circumference of the circle with this radius?
3. How do you find the diameter of the circle using the radius?
4. What would the area be if the radius were 12 m?
5. How is the area of a circle related to its radius mathematically?

**Tip:** Remember, the radius is half of the diameter of the circle.

Find the radius of a circle with an area of 262m^2. Round your answer to the nearest tenth.

Discover how to calculate the radius of a circle with an area of 262m^2 using the formula A = πr^2. This problem explores key geometric concepts such as the area of a circle and the use of square roots, making it suitable for students in Grades 6-8.

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