Question

The length of the minute hand of a clock is 6 cm. Find the area swept by the minute hand during the time period 8:05 am and 8:45 am. a) 1.5π cm² b) 3π cm² c) 4.5π cm² d) 6π cm²

Answer 1

The area swept by the minute hand is 4π cm².

Step-by-step explanation:

To find the area swept by the minute hand of a clock during a given time period, we need to determine the angle it sweeps and then calculate the area of the sector it creates.

From 8:05 am to 8:45 am, the minute hand moves 40 minutes in total. The minute hand moves 360 degrees in 60 minutes, so in 40 minutes it will move:

(40 / 60) * 360 = 240 degrees

The area of the sector can be calculated using the formula: (θ/360) * π * r². Substituting the values, we get:

(240/360) * π * (6)² = 4π cm²

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