The minute hand of a clock is 7
inches long and moves from 12 to 11
o'clock. How far does the tip of the minute hand move? Express your answer in terms of pi
and then round to two decimal places.
arc distanc=radius*angleinRadians
angleinRadians=11/12*2PI radians.
That is, if the clock is not running counterclockwise.
To find the distance the tip of the minute hand moves, we can use the circumference formula:
C = 2πr
where C is the circumference and r is the radius.
Given that the radius (length of the minute hand) is 7 inches, we can substitute this value into the formula:
C = 2π(7)
Simplifying further:
C = 14π
Now, we can calculate the circumference value:
C ≈ 43.98 inches
Therefore, the tip of the minute hand moves approximately 43.98 inches.
To calculate how far the tip of the minute hand moves, we need to determine the circumference of the circle that the tip traces as it moves from 12 to 11 o'clock.
The circumference of a circle can be calculated using the formula:
C = 2πr, where C is the circumference and r is the radius of the circle.
In this case, the radius of the circle is equal to the length of the minute hand, which is 7 inches.
So, the circumference of the circle traced by the tip of the minute hand is:
C = 2π(7) = 14π inches.
Since the question asks for the answer in terms of pi, we can leave it as 14π.
Rounding to two decimal places, 14π is approximately 43.98 inches.
The minute hand moves 35pi/6 inches
The minute hand moves approximately 18.33 inches