What is the area of a sector with a central angle of 120° and radius 8 cm?

Question

What is the area of a sector with a central angle of 120° and radius 8 cm?

1. A. \(64π/3\) cm² (Correct answer)
2. B. \(54π/3\) cm²
3. C. 48 cm²
4. D. 52 cm²

Correct Answer

Option A — \(64π/3\) cm²

Detailed Solution & Explanation

The correct answer is 64π/3 cm².

Key Points

• Area of a sector = (θ/360) × πr².
• Here θ = 120°, which is exactly one-third of a full circle, and r = 8:
  • (120/360) × π × 8² = (1/3) × π × 64
• That gives 64π/3 cm².

Additional Information

• The answer is left in terms of π, so no approximation is needed — check the options' form before deciding whether to substitute 22/7 or 3.14.
• Useful fractions of a circle: 90° = 1/4, 120° = 1/3, 60° = 1/6, 45° = 1/8, 180° = 1/2.
• The full circle here has area 64π ≈ 201 cm², so the sector at roughly 67 cm² is plainly a third of it — a quick check that rules out the numeric options 48 and 52.
• Where the options are expressed with π, leaving the answer in that form avoids rounding error entirely — substituting 22/7 here would give 67.02 and invite a mismatch.
• The sector's arc length is (120/360) × 2π × 8 = 16π/3 cm, and its perimeter adds the two radii, giving 16π/3 + 16 cm.

प्रश्न (हिन्दी में)

120° केन्द्रीय कोण तथा 8 सेमी त्रिज्या वाले त्रिज्यखंड का क्षेत्रफल क्या है?

1. A. \(64π/3\) सेमी²
2. B. \(54π/3\) सेमी²
3. C. 48 सेमी²
4. D. 52 सेमी²