How can I calculate the area of the shaded sector of a circle?

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To calculate the area of the shaded sector of a circle, you need two specific pieces of information: the radius of the circle and the angle of the sector in degrees or radians.

The formula to find the area of a sector is:

  • In degrees: Area = (θ / 360) * π * r2
  • In radians: Area = (1/2) * θ * r2

Where:

  • Area is the area of the shaded sector.
  • θ is the angle of the sector.
  • r is the radius of the circle.
  • π (Pi) is approximately 3.14159.

Step-by-Step Calculation:

  1. Determine the radius: Measure the distance from the center of the circle to the edge. Let’s say the radius (r) is 5 units.
  2. Identify the angle: Find out the angle of the sector. For example, if the angle (θ) is 90 degrees.
  3. Apply the formula: Using the degree formula, substitute r and θ into the formula:

    Area = (90 / 360) * π * (5)2

    Area = (1/4) * π * 25

    Area = 25π / 4 ≈ 19.635 square units.

Alternatively, if the angle was given in radians instead (for example, π/2 radians), you’d use the radians formula:

Area = (1/2) * (π/2) * (5)2
Area = (1/2) * (π/2) * 25
Area = 25π / 4 ≈ 19.635 square units.

In conclusion, by identifying the radius and the angle of the sector, you can easily determine the area of the shaded sector using the appropriate formula. Remember to use degrees or radians consistently to obtain the correct result!

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