Question

The minute hand of a clock is 7.5 cm long. Find the area of the face of the clock described by the minute hand in 56 minutes.

Answer 1

Given:

Length of minute hand (radius) r = 7.5 cm

Time = 56 minutes

Step-wise calculation:

1. Angle swept by minute hand: minute hand turns 360° in 60 min → in 1 min it turns 6°.

Angle θ = 56 × 6°

= 336°

2. Area of sector = `(θ/360) × πr^2`.

3. Substitute values: `θ/360 = 336/360`

= `14/15`

r² = (7.5)² 

= 56.25

Area = `14/15 xx π xx 56.25` 

= 52.5 π cm²

4. Numerical approximation:

Area ≈ 52.5 × 3.14159 ≈ 164.93 cm²

Area described by the minute hand in 56 minutes = 52.5 π cm² ≈ 164.93 cm².