Question 4 of 7intermediate🔧 ApplyNumerical3 marks

The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.

Correct Answer

The area swept by the minute hand in 5 minutes is 51.33 cm² (approximately).

Exercise: EXERCISE 11.1 | Q: 3 | (Chapter: Page 5)
For More Understanding

Explanation

This question tests the concept of area of a sector. The minute hand acts as the radius of a circle. In 60 minutes, the minute hand completes one full rotation (360°), so in 5 minutes, it sweeps an angle of 30°. Using the formula for area of sector with θ = 30° and radius = 14 cm, we calculate the swept area.

Solution Steps

  1. Step 1: Find the angle swept by minute hand in 5 minutes. In 60 minutes, angle = 360°. So in 5 minutes, angle = (5/60) × 360° = 30°.

  2. Step 2: Identify the radius. Length of minute hand = radius (r) = 14 cm.

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

  4. Step 4: Substitute values. Area = (30/360) × π × 14² = (1/12) × π × 196 = 49π/3 cm²

  5. Step 5: Calculate final answer using π = 22/7. Area = (49×2249 \times 22)/(3×73 \times 7) = 1078/21 = 51.33 cm² (approx.)

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