Question

In the circle shown below, ∠BAC is a central angle, r is the length of AB, and θ is the measure of ∠BAC in degrees.

Which of the following would be used to derive the formula for the area of sector BAC?

see attached picture and choices

Answer 1

Option 4 is the right answer.

Explanation:

As we know in the given circle area of minor segment having an angle ∅ and radius of the circle r is shown by

Area of the minor segment / Area of the circle = ∅ / 360° (∅ is in degrees)

Area of the minor segment / πr² = ∅ / 360°

Area of the minor segment = (∅ / 360°) × πr²

Therefore Option 4 is the right answer.