Question

The minute hand of a clock is 21 cm long. Calculate the area swept by it and the distance travelled by tip in 20 minutes.

Answer 1

Minute hand completes full circle in one hour.

So, angle swept by minute hand in 1 hour (i.e., 60 minutes) = 360°

∴ Angle swept by minute hand in 1 minute

= `360^circ/60^circ`

= 6°

Angle swept by minute hand in 20 minutes

= 6° × 20

= 120°

Hence, θ = 120°, r = 21 cm

Area swept by minute hand

= Area of sector

= `θ/360^circ xx πr^2`

= `120^circ/360^circ xx 22/7 xx (21)^2`

= `1/3 xx 22/7 xx 21 xx 21`

= 462 cm²

Distance travelled by minute hand

= `2πr (θ/360^circ)`   ...[Arc length]

= `2 xx 22/7 xx 21 xx 120^circ/360^circ`

= `2 xx 22 xx 3 xx 1/3`

= 44 cm