Question

In a clock, the minute hand is of length 7 cm. Find the area covered by the minute hand in 5 minutes.

Answer 1

Given:

Length of minute hand (radius) r = 7 cm

Time interval = 5 minutes

Central angle (θ) = `5/60 xx 360^circ = 30^circ`

Formula:

Area swept by the minute hand (A) = `θ/360^circ xx πr^2`

= `30^circ/(360^circ) xx 22/7 xx 7^2`

= `1/12 xx 22 xx 7`

= `154/12`

= `77/6`

≈ 12.83 cm²

The area covered by the minute hand in 5 minutes is 12.83 cm².