Answer:

The area swept by the minute hand from 9:00 a.m. to 9:10 a.m. is approximately 10.99 square cm

Explanation:

To find the area swept by the minute hand of a clock from 9:00 a.m. to 9:10 a.m., we need to determine the angle covered by the minute hand during that time period.

From 9:00 a.m. to 9:10 a.m., the minute hand moves from the 12 o'clock position to the 2-minute mark on the clock. Since there are 60 minutes on a clock and the minute hand completes a full revolution (360 degrees) in 60 minutes, we can calculate the angle covered by the minute hand as follows:

Angle covered per minute = 360 degrees / 60 minutes = 6 degrees per minute

The time from 9:00 a.m. to 9:10 a.m. is 10 minutes. Therefore, the total angle covered by the minute hand during this time period is:

Total angle covered = 6 degrees per minute * 10 minutes = 60 degrees

Now, let's calculate the area swept by the minute hand. The area swept by an arc of a circle is given by:

Area = (θ/360) * π * r^2

where θ is the angle (in degrees) and r is the length of the minute hand.

Plugging in the values, we have:

Area = (60/360) * π * (sqrt(21))^2

= (1/6) * π * 21

= (7/2) * π

≈ 10.99 square cm (rounded to two decimal places)

Therefore, the area swept by the minute hand from 9:00 a.m. to 9:10 a.m. is approximately 10.99 square cm.