Final answer:
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
Learn more about Calculating Area