The minute hand of a clock is 6 cm long. How far does the end of the hand the hand of the hand travel in 35 minutes
2 * π * 6 cm * 35/60
To find out how far the end of the minute hand travels in 35 minutes, we need to calculate the distance the tip of the hand moves along its circular path.
The length of the minute hand is given as 6 cm, which corresponds to the radius of the clock's circular face. Since the minute hand travels along the circumference of this circle, we need to calculate the circumference.
The formula for the circumference of a circle is C = 2πr, where C represents the circumference and r represents the radius.
In our case, the radius (length of the minute hand) is 6 cm. Plugging this value into the formula, we have:
C = 2π(6)
= 12π cm
Now, we know that the minute hand moves along this circumference in 60 minutes (one complete hour). Therefore, to find out how far it travels in 35 minutes, we need to calculate what fraction of the entire circumference corresponds to 35 minutes.
The proportion can be set up as follows:
35/60 = x/(12π)
To solve for x, we can cross-multiply:
35 * 12π = 60 * x
420π = 60x
Now, divide both sides of the equation by 60:
420π / 60 = x
7π = x
Therefore, the end of the minute hand travels a distance of 7π cm in 35 minutes.