1. What is Radius of Semicircle given Area of Circle?

The radius of a semicircle given the area of the full circle is calculated using the mathematical relationship between the area of a circle and its radius. Since a semicircle is exactly half of a full circle, but the area provided is for the full circle, we can directly compute the radius.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r \) — Radius of the semicircle (m)
• \( A_{Circle} \) — Area of the full circle (m²)
• \( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: The formula derives from the standard circle area formula \( A = \pi r^2 \), rearranged to solve for radius.

3. Importance of Radius Calculation

Details: Calculating the radius from the area is fundamental in geometry and various practical applications, including construction, engineering, and design where semicircular shapes are involved.

4. Using the Calculator

Tips: Enter the area of the full circle in square meters. The value must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: Why use the area of the full circle instead of the semicircle?
A: The formula is based on the relationship for a full circle. If you have the area of the semicircle, multiply it by 2 first to get the full circle area.

Q2: What if I have the area of the semicircle instead?
A: Multiply the semicircle area by 2 to get the full circle area, then use the calculator.

Q3: What units should I use?
A: The calculator uses meters for length and square meters for area. Ensure consistent units for accurate results.

Q4: Can this calculator handle very large or very small values?
A: Yes, as long as the input is a positive number, the calculator can process it.

Q5: Is the value of pi exact in the calculation?
A: The calculator uses PHP's built-in M_PI constant, which provides a high-precision value of pi.