35 min = 7/12 of an hour.
That is, 7/12 of the circumference of a circle with radius 6 cm.
so, ...
That is, 7/12 of the circumference of a circle with radius 6 cm.
so, ...
The minute hand of a clock moves in a circular motion with the center of the clock as the pivot point. The distance traveled by a point on a circle is equal to the circumference of the circle, which can be found using the formula:
Circumference = 2 * π * radius
In this case, the radius is equal to the length of the minute hand, which is given as 6 cm. So, the circumference of the circle is:
Circumference = 2 * π * 6 cm
Now, we need to find the distance traveled by the end of the hand for each minute. Since there are 60 minutes in an hour and the clock is divided into 12 equal sections, the minute hand will complete a full revolution around the clock (360 degrees) in 60 minutes.
Therefore, in one minute, the minute hand will travel:
Distance traveled in one minute = Circumference / 60
Plugging in the values, we have:
Distance traveled in one minute = (2 * π * 6 cm) / 60
Simplifying the equation gives:
Distance traveled in one minute = π * 6 cm / 30
Now, we can find the total distance traveled by the end of the minute hand in 35 minutes by multiplying the distance traveled in one minute by 35:
Total distance traveled in 35 minutes = Distance traveled in one minute * 35
Total distance traveled in 35 minutes = (Ï€ * 6 cm / 30) * 35
Simplifying the equation gives:
Total distance traveled in 35 minutes = π * 6 cm * 35 / 30
Calculating it gives:
Total distance traveled in 35 minutes ≈ 65.973 cm (rounded to three decimal places)
Therefore, the end of the minute hand travels approximately 65.973 cm in 35 minutes.