The Area of a Segment of a Circle Calculator is a tool designed to find the area of a segment within a circle. This tool is particularly useful when dealing with geometric calculations involving circles. By inputting the required parameters, the calculator swiftly computes the area of the segment, providing a quick and accurate result.
Formula of Area of a Segment of a Circle Calculator
The formula utilized by the calculator is:
A = (θ/360) * π * r² - (1/2) * r² * sin(θ)
Where:
Arepresents the area of the segment.θdenotes the central angle of the segment in degrees.π(pi) is a constant approximately equal to 3.14159.rsignifies the radius of the circle.sin(θ)calculates the sine of the central angleθ, achievable using a scientific calculator or software.
This formula efficiently computes the segment’s area based on the specified inputs.
General Terms
Here’s a table encompassing general terms related to circle segment calculations that individuals often search for:
| Term | Description |
|---|---|
| Circle Segment | A section of a circle between a chord and the arc. |
| Central Angle | The angle subtended by an arc at the center of a circle. |
| Radius | The distance from the center of the circle to any point on its circumference. |
This table serves as a quick reference guide for users, aiding them in understanding the essential terms related to circle segments.
Example of Area of a Segment of a Circle Calculator
Let’s consider an example to better grasp the application of the formula:
Suppose we have a circle with a radius of 8 units. If the central angle of the segment is 45 degrees, we can calculate the area of the segment using the formula:
A = (45/360) * π * 8² - (1/2) * 8² * sin(45)
This calculation will yield the area of the segment, offering a practical example of how the calculator operates.
Most Common FAQs
A: No, this calculator specifically computes the area of a segment within a circle. For the area of a circular sector, a different formula is utilize.
A: If incorrect values are input, the calculator might display an error message. Ensure the radius and central angle are entered correctly for accurate results.