Question 21 of 42intermediate🔧 ApplyNumerical3 marks

The length of the minute hand of a clock is 7 cm. Find the area swept by the minute hand in 10 minutes.

Correct Answer

77/3 cm²

Exercise: Exercise Set 6.3 | Q: 3 | (Page 31)
For More Understanding

Explanation

The minute hand of a clock acts as the radius of a circular sector. In 60 minutes, the minute hand completes a full rotation of 360°, meaning it sweeps 60° in 10 minutes. By applying the sector area formula with the given radius and the standard approximation for pi, we calculate the required area.

Solution Steps

  1. Step 1: Determine the angle swept in 10 minutes. In 60 minutes, the minute hand sweeps 360°. So, in 10 minutes, Angle (θ) = (10 / 60) × 360° = 60°.

  2. Step 2: Identify the radius of the sector. The length of the minute hand is the radius, so Radius (r) = 7 cm.

  3. Step 3: Apply the formula for the area of a sector: Area = (θ / 360) × πr².

  4. Step 4: Substitute the values using π ≈\approx 22/7. Area = (60 / 360) × (22 / 7) × (7)² = (1 / 6) × (22 / 7) × 49 = (1 / 6) × 22×722 \times 7 = 154 / 6 = 77/3 cm².

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