Question

The minute hand of a wall clock is 18 cm long. Find the area of the face of the clock described by the minute hand in 35 minutes.

Answer 1

The minute hand sweeps 35 minutes.

Angle Swept by minute hand in 60 minutes = 360°

Angle Swept by minute hand in 1 minute = `(360°)/(60°)`

Angle Swept by minute hand in 35 minutes = `(360°)/(60°) xx 35`

= 6 × 35°

= 210° 

Hence,

θ = 210°, r = 18 cm

Now,

Area Swept by minutes hand = Area of sector

= `θ/(360°) xx πr^2`

= `(210°)/(360°) xx 22/7 xx (18  cm)^2`

= `(210°)/(360°) xx 22/7 xx 18 xx 18  cm^2`

= 11 × 3 × 18 cm²

= 594 cm²