Question

The length of the minute hand of clock is 14 cm. Find the area swept by the minute hand in 15 minutes.

Answer 1

Minute hand completes full circle degree in 1 hour.

So, degree swept by minute hand in 1 hour (60 minutes) = 360°

∴ Degree swept by minute hand in 1 minute = `360^circ/60` = 6° and degree swept by minute hand in 15 minutes

= 6° × 15°

= 90°

Hence, θ = 90° and r = 14 cm

Area swept by minute hand = Area of sector

= `θ/360^circ xx πr^2`

= `90^circ/360^circ xx 22/7 xx (14)^2`

= `1/4 xx 22/7 xx 14 xx 14`

= 154 cm²