From a circle with a radius of 15.75 cm, a sector with an arc length of 11 cm is cut off. Find the area (in cm²) of this sector.

Question

Accepted Answer

Let the radius of the circle be r = 15.75 cm and the arc length of the sector be l = 11 cm.

The arc length of a sector is given by:
  l = θ/360 × 2πr
where θ is the central angle in degrees.

First, solve for θ:
  11 = θ/360 × 2 × π × 15.75
  11 = θ/360 × 2 × 3.14 × 15.75
  11 = θ/360 × 98.955
  θ/360 = 11 / 98.955
  θ = (11 / 98.955) × 360
  θ ≈ 0.1112 × 360
  θ ≈ 40.032°

Now, area of the sector = θ/360 × πr²
  Area = (40.032/360) × 3.14 × (15.75)²
  (15.75)² = 248.0625
  Area = (0.1112) × 3.14 × 248.0625
  Area ≈ 0.1112 × 779.89925
  Area ≈ 86.625 cm²

Thus, the area of the sector is 86.625 cm².

Answer

Answer

Answer