Final answer:
The area swept by the minute hand from 6:05 am to 6:40 am is 45 5/6 cm². This is calculated by finding the angle of sweep the minute hand covers in 35 minutes and then using the formula for the area of a sector of a circle. So the correct answer is Option D.
Step-by-step explanation:
To calculate the area swept by the minute hand from 6:05 am to 6:40 am, we first determine the angle of sweep. Since the minute hand moves 360 degrees in 60 minutes, we can calculate the proportion for 35 minutes (from 6:05 am to 6:40 am) which is (35/60) × 360 degrees. Now, the area swept by the minute hand can be found using the formula for the area of a sector of a circle:
Area of sector = (θ/360) × π × r²
Plugging in θ (the angle in degrees) and r (radius of 5 cm), we get:
Area = (35/60) × 360/360 × π × 5²
= (35/60) × π × 25
= (35/60) × 78.54 (using π ≈ 3.14)
= 45.85 cm²
When converting to a mixed number, we get 45 17/20 cm², which needs to be simplified:
45 17/20 = 45 5/6 cm²
Therefore, the correct answer is D 45 5/6 cm².