Find the perimeter of a circle if its area is 706.5 cm²

To find the perimeter (circumference) of a circle when its area is given, follow these steps:

1. **Formula for the area of a circle:**
   \[
   A = \pi r^2
   \]
   where \( A \) is the area and \( r \) is the radius.

2. Plug the given area into the formula:
   \[
   706.5 = \pi r^2
   \]

3. Solve for \( r \) (radius):
   \[
   r^2 = \frac{706.5}{\pi}
   \]
   \[
   r = \sqrt{\frac{706.5}{\pi}}
   \]

4. **Formula for the circumference (perimeter) of a circle:**
   \[
   C = 2\pi r
   \]

Let's calculate this step by step.The perimeter (circumference) of the circle is approximately \( 94.22 \) cm.

Would you like further details on the steps, or do you have any additional questions?

Here are 5 related questions to expand your understanding:

1. How would the perimeter change if the area were doubled?
2. Can you calculate the diameter of the circle using the given area?
3. What is the formula for the area of a sector of a circle?
4. How does the circumference relate to the diameter of a circle?
5. How do you calculate the perimeter of a semicircle?

**Tip:** The ratio of the circumference to the diameter of any circle is always \( \pi \), a key property of all circles.

Learn how to find the perimeter (circumference) of a circle given its area of 706.5 cm². This problem explores key geometric concepts like the area and perimeter formulas for circles. Suitable for students in Grades 8-10.

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