The central angle of a sector is 80° and the length of the sector is 96π. What is the radius of the circle?

Question

Accepted Answer

Given:
- Central angle (θ) = 80°
- Length of sector (arc length) = 96π

Formula for arc length of a sector:
Arc length = (θ/360) × 2πr

Substitute the values:
96π = (80/360) × 2πr

Simplify the fraction:
80/360 = 2/9

So,
96π = (2/9) × 2πr
96π = (4/9)πr

Divide both sides by π:
96 = (4/9)r

Multiply both sides by 9:
96 × 9 = 4r
864 = 4r

Divide both sides by 4:
r = 864 / 4 = 216

Check calculation carefully:
There seems to be a discrepancy; re-check the fraction:
80/360 = 2/9 correct.

Arc length = (2/9) × 2πr = (4/9)πr

So,
96π = (4/9)πr
Divide both sides by π:
96 = (4/9)r
Multiply both sides by 9:
864 = 4r
r = 864 / 4 = 216

Therefore, the radius is 216 units.

Since 216 units is option 4, the correct answer is 216 units.

Answer

Answer

Answer