Part 1. Imagine a clock without the hour hand, When clock strikes 3:35, the minute hand is at 7. When it strikes 3:55, the minute hand is in 11. Each gap between two adjacent digits in the clock measures 30°. This is because a revolution divided by 12 is 360/12 = 30. Then, the angle between the minute hands in the picture is equal to 4(30°) = 120°. Know that π radians is equal to 180°. Converting 120° to radians,
120°(π radians/180°) = (2/3)π or 2.09 radians
Part 2. For this part, we determine the arc length intercepted by the angle 120° because this is the total distance travelled by the tip of the minute hand.
S = rθ, where θ is the angle in radians and r is the radius of the circle represented by the minute hand.
S = (4)(2.09)
S = 8.36 inches
Hence, the tip of the minute hand travelled a total distance of 8.36 inches.
120°(π radians/180°) = (2/3)π or 2.09 radians
Part 2. For this part, we determine the arc length intercepted by the angle 120° because this is the total distance travelled by the tip of the minute hand.
S = rθ, where θ is the angle in radians and r is the radius of the circle represented by the minute hand.
S = (4)(2.09)
S = 8.36 inches
Hence, the tip of the minute hand travelled a total distance of 8.36 inches.