Question 5 of 42beginner🔧 ApplyNumerical3 marks

Find the area of a sector of a circle with radius 7 cm if the angle of the sector is 60°.

Correct Answer

77/3 cm² or 25.67 cm²

Exercise: Exercise Set 6.3 | Q: 1 | (Chapter: 31)
For More Understanding

Explanation

The area of a sector of a circle is calculated using the formula derived from the rotational symmetry of a circle: Area = πr² × (θ/360°). Given the radius r = 7 cm and the sector angle θ = 60°, we substitute these values into the formula. As instructed in the textbook context, we use the approximation π ≈\approx 22/7. This allows for easy cancellation of the 7 in the radius squared.

Solution Steps

  1. Given: Radius (r) = 7 cm, Angle of sector (θ) = 60°, and π = 22/7

  2. Formula: Area of sector = πr² × (θ/360°)

  3. Substitution: Area = (22/7) × (7)² × (60/360)

  4. Calculation: Area = (22/7) × 49 × (1/6) = 22×722 \times 7 × (1/6) = 154/6 = 77/3

  5. Result: The area of the sector is 77/3 cm² (or approximately 25.67 cm²).

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