a. the distance traced by the minute hand between the 12 (o’clock) and the 4 is 2.09 in
b. The distance traced by the hour hand between the 12 (o’clock) and the 4 is 10.47 in
Since A clock’s minute hand is 10 inches long. The hour hand is half as long as the minute hand.
a. What is the distance traced by the minute hand between the 12 (o’clock) and the 4?
To find the distance moved by the minute from 12 (o’clock) and the 4, we use the length of an arc
L = Ф/360 × 2πr where
- Ф = distance moved from 12 (o'clock) to 4 = 360°/3 = 120°
- r = length of minute hand = 10 in
So, substituting the values of the variables into the equation, we have that
L = Ф/360 × 2πr
L = 120°/360 × 2π(10 in)
L = 1/3 × 2π in
L = 1/3 × 6.283 in
L = 2.094 in
L ≅ 2.09 in
b. What is the distance traced by the hour hand in the same angle?
Since the hour hand is half as long, using the same formula for length of arc the distance moved by the hour hand from 12 (o’clock) and the 4
L = Ф/360 × 2πr where
- Ф = distance moved from 12 (o'clock) to 4 = 360°/3 = 120°
- r = length of minute hand = 10 in/2 = 5 in
So, substituting the values of the variables into the equation, we have that
L = Ф/360 × 2πr
L = 120°/360 × 2π(5 in)
L = 1/3 × 10π in
L = 1/3 × 31.416 in
L = 10.472 in
L ≅ 10.47 in