Final answer:
The area of the face of a clock described by the minute hand at 9:00 a.m. is 36π cm², as calculated using the formula for the sector area with a 90-degree angle and a 12 cm radius.
Step-by-step explanation:
The student has asked about calculating the area of the face of a clock that is described by the minute hand when the clock shows 9:00 a.m. At 9:00 a.m., the minute hand points at the 12 and the hour hand points at the 9. At this time, the angle between the hour hand and minute hand is 90 degrees because each hour represents 30 degrees on the clock's face (360 degrees in a full circle divided by 12 hours).
To determine the area swept by the minute hand from 12 to 9, one can consider this area to be a sector of a circle (the clock face), where the radius is the length of the minute hand, which is 12 cm. The area of a sector is calculated using the formula Area = (θ/360) × π × r2, where θ is the central angle in degrees and r is the radius of the circle. In our case, θ is 90 degrees and r is 12 cm.
Therefore, the area described by the minute hand at 9:00 a.m. can be found by plugging these values into the formula: Area = (90/360) × π × (12 cm)2 = π × 36 cm2 = 36π cm2. The area of the face of the clock described by the minute hand at 9:00 a.m. is therefore 36π cm2.