Find the measure of the central angle of a sector if its area is 16π and the radius is 8.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 90°.
Area of a sector (A) = (θ/360°)πr2
Where θ is the central angle in degrees and r is the radius of the circle
So, (θ/360°) × π(82) = 16π
⇒ (θ/360°) × 64π = 16π
⇒ θ = (1/4) × 360° = 90°
Therefore, the measure of the central angle is 90°.