Question

The minute hand of a clock is 12 cm long. Find the area of the face of the clock described by the minute hand in 35 minutes.

Answer 1

Angle described by the minute hand in 60 minutes = 360°

Angle described by the minute hand in 35 minutes = `(360/60 xx 35)^circ` = 210°

Now, r = 12 cm and θ = 210°

∴ Required area described by the minute hand in 35 minutes = Area of the sector where r = 12 cm and θ = 210°

= `(πr^2θ)/(360^circ)`

= `(22/7 xx (12 xx 12 xx 210^circ)/360^circ) cm^2`

= `665280/2520`

= 264 cm²