The 100-foot clock tower in Rome, Georgia is more than 100 feet tall. The minute hand is 4 feet, 3 inches long, and the hour hand is 3 feet, 6 inches long. How many inches farther does the tip of the minute hand travel than the tip of the hour hand in one day?
I'm not quite sure how to do this, but I have a few things that I know: the minute hand HAS to travel more because it moves more than the hour hand. The circumference (if drawn) with radius of the minute hand will be 102pi inches and the the circumference (if drawn) for the hour hand will be 84pi inches. Not sure where to.go from there.
just subtract the smaller circumference from the larger. The difference is how much farther the longer hand travels.
Odd, how you did the hard part, but then got stuck on the simple subtraction.
To calculate the distance traveled by the tip of each hand in one day, we need to find the circumference that each hand traces during that time.
First, let's convert the measurements to a common unit. Both the minute hand and the hour hand are measured in feet and inches, so let's convert everything to inches to make the calculations easier.
The minute hand is 4 feet and 3 inches long, which is equivalent to (4 * 12) + 3 = 51 inches.
The hour hand is 3 feet and 6 inches long, which is equivalent to (3 * 12) + 6 = 42 inches.
Next, we need to calculate the circumference traced by each hand. The circumference of a circle can be found using the formula:
Circumference = 2 * π * radius
For the minute hand, the radius is equal to the length of the hand, so the circumference is:
Minute Hand Circumference = 2 * π * 51 inches = 102π inches
For the hour hand, the radius is equal to the length of the hand, so the circumference is:
Hour Hand Circumference = 2 * π * 42 inches = 84π inches
Now, let's calculate the difference in distance traveled by the tip of the minute hand compared to the tip of the hour hand in one day.
Since both hands complete one full rotation (i.e., 360 degrees) in 12 hours, we can calculate the proportion of the total circumference each hand travels in one day.
Minute Hand Distance = (102π inches / 360 degrees) * 360 degrees = 102π inches
Hour Hand Distance = (84π inches / 360 degrees) * 360 degrees = 84π inches
Therefore, the tip of the minute hand travels 102π inches, while the tip of the hour hand travels 84π inches in one day.
To find the difference between the distances traveled, we subtract the distance of the hour hand from the distance of the minute hand:
Difference = 102π inches - 84π inches = 18π inches
So, the tip of the minute hand travels 18π inches farther than the tip of the hour hand in one day.
Note: The value of π is approximately 3.14, so the final answer in inches will depend on the accuracy level required in the calculation.