The area of a sector of a circle with radius 7 cm and central angle 90° is:

Question

The area of a sector of a circle with radius 7 cm and central angle 90° is:

1. A. 38.5 cm² (Correct answer)
2. B. 35.2 cm²
3. C. 40.5 cm²
4. D. 42.62 cm²

Correct Answer

Option A — 38.5 cm²

Detailed Solution & Explanation

The correct answer is 38.5 cm².

Key Points

• Area of a sector = (θ/360) × πr².
• With θ = 90° the sector is exactly a quarter circle:
  • (90/360) × (22/7) × 7² = (1/4) × (22/7) × 49
• (22/7) × 49 = 154, and a quarter of 154 = 38.5 cm².

Additional Information

• A radius of 7 (or any multiple of 7) is chosen so that π = 22/7 cancels cleanly — treat it as a signal to use the fraction rather than 3.14.
• Related formulae: arc length = (θ/360) × 2πr, and the perimeter of a sector = arc length + 2r, which is a common follow-up question.
• The full circle here has area 154 cm² and circumference 44 cm, both worth noting since a 7 cm radius recurs constantly in SSC mensuration.

प्रश्न (हिन्दी में)

7 सेमी त्रिज्या और 90° के केंद्रीय कोण वाले एक वृत्त के त्रिज्यखंड का क्षेत्रफल है:

1. A. 38.5 सेमी²
2. B. 35.2 सेमी²
3. C. 40.5 सेमी²
4. D. 42.62 सेमी²