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 → angle swept = `5/60 xx 360^circ = 30^circ`.

Step-wise calculation:

1. Use area of a sector:

`A = θ/360^circ xx πr^2`

2. Substitute θ = 30° and r = 7 cm:

`A = 30/(360^circ) xx π xx 7^2`

= `1/12 xx π xx 49`

= `(49π)/12` cm²

3. Numerical value:

`(49π)/12 ≈ 12.83` cm²   ...(Rounded to two decimal places)

Area covered by the minute hand in 5 minutes = `(49π)/12` cm² ≈ 12.83 cm².