If in the figure below, angle XYZ = 90° and the length of the arc XZ = 10π

Geometry

If in the figure below, angle XYZ = 90° and the length of the arc XZ = 10π, then the area of the sector XYZ is

  1. 10π
  2. 25π
  3. 100π
  4. None of the above

Solution

Y is the centre of the circle. Let r be the radius of the circle.

Length of arc XZ = ¼ × 2?r = 10?

r = 20

Arc of sector XYZ = ¼ × ?r2 = 100?

The correct option is C.