About Circular Sector Area Calculation

What is a Circular Sector?

A circular sector is a portion of a circle enclosed by two radii and an arc. It resembles a "pie slice" and is defined by its radius and the central angle it subtends.

Formula for Circular Sector Area

The formula to calculate the area of a circular sector is:

\[A = \frac{\theta}{360°} \pi r^2\]

Where:

• \(A\) is the area of the circular sector
• \(\theta\) (theta) is the central angle in degrees
• \(\pi\) (pi) is approximately 3.14159
• \(r\) is the radius of the circle

Calculation Steps

1. Identify the radius (r) of the circle.
2. Determine the central angle (θ) in degrees.
3. Divide the central angle by 360°.
4. Multiply the result by π (pi).
5. Multiply by the square of the radius.
6. The final result is the area of the circular sector in square units.

Example

Let's calculate the area of a circular sector with a radius of 5 units and a central angle of 60°:

1. Given:
   • Radius (r) = 5 units
   • Central Angle (θ) = 60°
2. Apply the formula: \(A = \frac{\theta}{360°} \pi r^2\)
3. Substitute the values: \(A = \frac{60°}{360°} \pi (5)^2\)
4. Calculate:
   \(A = \frac{1}{6} \pi (25)\)
   \(A = \frac{25\pi}{6}\)
   \(A \approx 13.09\) square units (rounded to 2 decimal places)

Visual representation:

Therefore, the area of the circular sector is approximately 13.09 square units.