A clock has a minute hand10 inches long. What is the distance traveled by the tip of the minute hand in 1 day?
2 pi *10 inches per hour
one day is 24 hours two rotations on the clock. Each rotation is equal to 2 pi. then it will be 2 times 2 times pi.
apply the formula with radius equal to 10 inches:
S = r * central angle in radians
S = 10 * 4 * pi
S = 125.6 inches
To determine the distance traveled by the tip of the minute hand in 1 day, we need to calculate the circumference of the circle formed by the movement of the hand and multiply it by the number of complete rotations made in one day.
The minute hand of a clock completes a full rotation every 60 minutes, which is equivalent to one hour. Since there are 24 hours in a day, the minute hand will complete 24 full rotations in a 24-hour period.
To calculate the circumference of the circle formed by the minute hand, we can use the formula: circumference = 2 * π * radius
Given that the length of the minute hand is 10 inches, the radius is equal to half of this value, which is 5 inches.
Therefore, the circumference is: 2 * π * 5 inches = 10π inches
To find the distance traveled by the tip of the minute hand in 1 day, we multiply the circumference by the number of rotations:
Distance = 10π inches * 24 rotations = 240π inches
So, the tip of the minute hand travels a distance of 240π inches in 1 day.