Find the measure of the central angle of a sector if its area is 16π and the radius is 8.

Question

Accepted Answer

The area of a sector of a circle is given by the formula: (θ/360) × πr², where θ is the central angle in degrees and r is the radius.

Given:
Area = 16π
Radius, r = 8

Using the formula:
(θ/360) × π × 8² = 16π
(θ/360) × π × 64 = 16π
(θ/360) × 64 = 16
θ/360 = 16/64
θ/360 = 1/4
θ = 360 × 1/4 = 90°

Therefore, the measure of the central angle is 90°.

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