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

Length of minute hand: 9m

Angle moved in one hour = 360°
Distance = (360/360)*2*π*9m=18π m
Length of hour hand: 9m*2/3=6m
Angle moved in one hour = 360/12=30°
Distance = (30/360)*2*π*6 = π m

Calculate the difference.

To calculate the distance traveled by each clock hand in one hour, we need to know their respective speeds.

The minute hand completes a full rotation every 60 minutes or 360 degrees in one hour. The formula to calculate the distance traveled by a rotating object is:

Distance = (2 * π * r * θ) / 360

where r is the radius (length) of the hand and θ is the angle traveled in degrees.

Let's calculate the distance traveled by the minute hand first:
- Length of the minute hand = 9 meters
- Radius of the minute hand = Length of the minute hand = 9 meters
- Angle traveled by the minute hand in one hour = 360 degrees

Substituting these values into the formula:
Distance = (2 * π * 9 * 360) / 360 = 18π meters

Now, let's calculate the distance traveled by the hour hand:
- Length of the hour hand = (2/3) * Length of the minute hand = (2/3) * 9 meters = 6 meters
- Radius of the hour hand = Length of the hour hand = 6 meters
- Angle traveled by the hour hand in one hour = 360 degrees

Substituting these values into the formula:
Distance = (2 * π * 6 * 360) / 360 = 12π meters

To find the difference in distance traveled by the minute hand and the hour hand in one hour, subtract the distance traveled by the hour hand from the distance traveled by the minute hand:

Difference = Distance of minute hand - Distance of hour hand

Difference = (18π meters) - (12π meters) = 6π meters

Therefore, in one hour, the minute hand will travel an additional distance of 6π meters compared to the hour hand.