Q 10 - The region of a circle is 24.64m2. The circuit of the circle is:

To find the circumference (or circuit) of a circle given its area, we can use the following formulas:

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

2. **Circumference of a circle:**  
\[
C = 2 \pi r
\]
where \( C \) is the circumference.

Given:
\[
A = 24.64 \, \text{m}^2
\]

### Step 1: Solve for the radius \( r \)

We can rearrange the area formula to solve for \( r \):

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

Substitute the given area:

\[
r = \sqrt{\frac{24.64}{\pi}}
\]

### Step 2: Calculate the circumference \( C \)

Once we find \( r \), we substitute it into the circumference formula:

\[
C = 2 \pi r
\]

Let's calculate these values.The radius of the circle is approximately \(2.80\) meters.  
The circumference (circuit) of the circle is approximately \(17.60\) meters.

Would you like more details or have any questions?

### Related Questions:
1. How do you derive the formula for the area of a circle?
2. What is the relationship between a circle's diameter and its circumference?
3. How can you find the diameter if the area of a circle is given?
4. What is the value of \( \pi \) and why is it important in circle-related formulas?
5. How do you calculate the area and circumference of a sector of a circle?

**Tip:** When solving problems related to circles, always make sure to identify which quantities are given and use the appropriate formulas accordingly.

Q 10 - The region of a circle is 24.64m2. The circuit of the circle is:

Learn how to find the circumference of a circle with an area of 24.64 m² using geometric formulas. This problem involves key concepts in circle geometry, including the area formula A = πr² and the circumference formula C = 2πr. Suitable for students in Grades 6-8.

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