1. What is the Radius of Quarter Circle Formula?

The formula calculates the radius of a quarter circle when the area is known. It is derived from the standard area formula of a full circle and adjusted for a quarter section.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r \) — Radius of Quarter Circle (m)
• \( A \) — Area of Quarter Circle (m²)
• \( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula rearranges the quarter circle area formula \( A = \frac{1}{4} \pi r^2 \) to solve for the radius.

3. Importance of Radius Calculation

Details: Calculating the radius from a known area is essential in geometry, engineering, and design applications where quarter circle shapes are used.

4. Using the Calculator

Tips: Enter the area of the quarter circle in square meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a quarter circle?
A: A quarter circle is one-fourth of a full circle, formed by two radii at right angles and the arc connecting them.

Q2: How is this formula derived?
A: Starting from the full circle area formula \( A_{full} = \pi r^2 \), the quarter circle area is \( A = \frac{1}{4} \pi r^2 \). Solving for r gives \( r = \sqrt{\frac{4A}{\pi}} \).

Q3: What units should I use?
A: Use consistent units (typically meters for radius and square meters for area). The calculator will return results in the same unit system.

Q4: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal values for area with up to 4 decimal places precision.

Q5: What if I get an error message?
A: Ensure you've entered a positive numerical value for the area. Negative values and zero are not valid inputs.