Arc length

Use the sector-perimeter formula P = 2r + s, because the boundary contains two radii and one arc. With P = 32 cm and s = 12 cm, we obtain 32 = 2r + 12. Thus 2r = 20 and r = 10 cm. In radian measure, arc length satisfies s = rθ, so θ = s/r = 12/10 = 6/5 radians. Therefore option B is correct. The fraction 5/6 reverses the required ratio and would correspond to r/s rather than s/r. The other choices are not supported by either the perimeter equation or the arc-length formula. Substitution also checks the result: 10 × 6/5 = 12 and 2(10) + 12 = 32.