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The formula \( r = \frac{l_{Arc}}{\pi} \) calculates the radius of a semicircle when the arc length is known. This formula is derived from the relationship between the circumference of a full circle and its radius.
The calculator uses the formula:
Where:
Explanation: The arc length of a semicircle is exactly half the circumference of a full circle, which is \( \pi r \). Therefore, the arc length equals \( \pi r \), and solving for r gives \( r = \frac{l_{Arc}}{\pi} \).
Details: Calculating the radius from the arc length is essential in geometry, engineering, and various design applications where semicircular shapes are involved. It helps in determining the size and proportions of semicircular structures and components.
Tips: Enter the arc length of the semicircle in meters. The value must be positive and greater than zero for accurate calculation.
Q1: Why is π used in the formula?
A: π is the ratio of the circumference of a circle to its diameter, making it fundamental in all circle-related calculations, including semicircles.
Q2: Can this formula be used for full circles?
A: For a full circle, the arc length would be the full circumference, which is \( 2\pi r \), so the formula would be \( r = \frac{C}{2\pi} \), where C is the circumference.
Q3: What units should be used for the arc length?
A: The arc length should be in meters, but any consistent unit of length can be used as long as the radius will be in the same unit.
Q4: Is the formula applicable to all semicircles?
A: Yes, the formula applies to any perfect semicircle, regardless of size, as long as the arc length represents half the circumference of a circle.
Q5: How accurate is the calculation?
A: The accuracy depends on the precision of the input value and the mathematical constant π used in the calculation. The calculator uses a high-precision value of π for accurate results.