A sector has perimeter 32 cm and arc length 12 cm. What is its central angle in radians?
Answer and explanation
Correct answer: 6/5
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.
Frequently asked questions
What is the correct answer to this question?
6/5
Why is this the correct answer?
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.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Area and Perimeter. Topic: Arc length.
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