the minute hand of a clock is 6cm long how far does the end of the hand travel in 35 minutes
35/60 of the circumference of a complete circle of radius 6 cm.
To determine how far the end of the minute hand travels in 35 minutes, we can make use of the formula:
Distance = Circumference of the Circle * (Angle/360)
First, let's find the circumference of the circle. The circumference of a circle can be found using the formula:
Circumference = 2 * π * radius
Given that the length of the minute hand is 6 cm, we can use this as the radius. Thus:
Circumference = 2 * π * 6 cm
Simplifying this, we find:
Circumference = 12π cm
Now, let's find the angle traveled by the minute hand in 35 minutes. In a clock, the minute hand completes one full rotation of 360 degrees in 60 minutes. Therefore, in 35 minutes:
Angle = (35/60) * 360 degrees
Simplifying this, we find:
Angle = 210 degrees
Now we can plug in the values into the distance formula:
Distance = 12π cm * (210 degrees / 360)
Calculating this value, we find that the end of the minute hand travels approximately:
Distance ≈ 38.84 cm
Therefore, the end of the hand travels about 38.84 cm in 35 minutes.