the minute hand of a clock is 9cm long. the hour hand clock is 2/3 times longer than the minute clock. how much more distance will minute hand clock move than hour clock in 1 hour?

2pi Rminute - 2 pi Rhour/12

How far does the tip of the minute hand move from 2:45pm to 3:25 p? The minute hand is 7.8 feet from its point of rotation. Answer to the nearest 10th of a foot.

To calculate the distance traveled by each clock hand in one hour, we need to understand the concept of angular speed. The minute hand moves 360 degrees in 60 minutes (1 hour), and the hour hand moves 360 degrees in 12 hours.

First, let's find the length of the hour hand. We know that it is 2/3 times longer than the minute hand, which is 9 cm. So, the length of the hour hand will be (2/3) * 9 cm.

Therefore, the length of the hour hand is (2/3) * 9 = 6 cm.

Now, we can calculate the distance traveled by each hand in one hour. The distance a clock hand travels is given by the formula:

Distance = (2π * r * θ) / 360

Where:
- r is the length of the clock hand
- θ is the angle covered by the clock hand

For the minute hand:
Length of the minute hand (r) = 9 cm
Angle covered by the minute hand (θ) = 360 degrees

For the hour hand:
Length of the hour hand (r) = 6 cm
Angle covered by the hour hand (θ) = 30 degrees (360 degrees divided by 12 hours)

Now, we can calculate the distances traveled by each hand:

Distance traveled by the minute hand = (2π * 9 * 360) / 360 = 18π cm

Distance traveled by the hour hand = (2π * 6 * 30) / 360 = π cm

To find how much more distance the minute hand travels compared to the hour hand, we subtract the distance traveled by the hour hand from the distance traveled by the minute hand:

Difference = 18π cm - π cm

Difference = 17π cm

Therefore, the minute hand will travel 17π cm more than the hour hand in one hour.