To find the circumference of the circular sign, we first need to determine its radius using the given area. The formula for the area \(A\) of a circle is:
\[A = \pi r^ 2\]
Given \(A = 69.3626\) square inches and \(\pi = 3.14\), we can solve for the radius \(r\):
\[69.3626 = 3.14 r^ 2\]
\[r^ 2 = \frac { 69.3626} { 3.14} \]
\[r^ 2 \approx 22.1\]
\[r \approx \sqrt { 22.1} \]
\[r \approx 4.70\]
Now, we use the radius to find the circumference \(C\) of the circle. The formula for the circumference is:
\[C = 2 \pi r\]
Using \(\pi = 3.14\) and \(r \approx 4.70\):
\[C = 2 \times 3.14 \times 4.70\]
\[C \approx 29.48\]

Supplemental Knowledge

In geometry, the area and circumference of a circle are fundamental properties that can be calculated using the radius or diameter. The formulas are:

• \[Area ( A) : A = \pi r^ 2\], where \(r\) is the radius.
• \(Circumference ( C) \): \(C = 2 \pi r\).
  Given the area, you can find the radius first and then use it to find the circumference.

Concepts to Actions

Imagine designing a circular garden bed in your backyard. Knowing how to calculate area and circumference helps determine how much soil will be needed while planning around materials like fencing or edging around its edge can ensure sufficient resources and help budget your project efficiently.
For example, if your garden bed has an area of 69.3626 square feet, similar to our problem here, you'd follow similar steps to find out how much fencing material you'll need to enclose it.

Understanding geometric properties of circles is essential for various practical applications, from designing spaces to solving real-world problems. At UpStudy, we offer tools and resources that help you master these concepts effectively.
For detailed guidance on geometry, explore UpStudy’s Geometry calculator today!