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

Points to Remember:

• The area covered by the minute hand represents a sector of a circle.
• The formula for the area of a sector is (θ/360) * πr², where θ is the central angle in degrees and r is the radius.
• The minute hand completes a full circle (360°) in 60 minutes.

Introduction:

This question requires a factual and analytical approach to determine the area swept by the minute hand

of a clock in a given time. The problem involves calculating the area of a sector of a circle. The minute hand, with a length of 14 cm, acts as the radius of the circle. We need to determine the angle swept by the minute hand in 5 minutes and then use this angle to calculate the area of the sector.

Body:

1. Calculating the Angle:

The minute hand completes a full rotation (360°) in 60 minutes. Therefore, in 5 minutes, it covers (5/60) * 360° = 30°.

2. Calculating the Area of the Sector:

The area of a sector is given by the formula: Area = (θ/360) * πr²

Where:

• θ = central angle (in degrees) = 30°
• r = radius = length of the minute hand = 14 cm
• π ≈ 3.14159

Substituting the values:

Area = (30/360) * π * (14)²
Area = (1/12) * π * 196
Area ≈ (1/12) * 3.14159 * 196 Subscribe on YouTube