The minute hand is 12 feet long, but the clock face is 22 feet in diameter.
If the minute hand were twice as long, how much farther would it travel every hour?
In one hour the minute hand makes one revolution or one circumference.
if the minute had is 12 ft long, then the circumference is 2π(12) or 24π feet
if the minute had were 24 feet long, it would travel
2π(24) or 48π ft
which would be 24π ft farther.
BTW, that is one huge clock!
and the end of the minute hand would stick out way beyond the clock face.
You sure you don't have a typo here ?
It does seem like a typo to me too but that's what the paper says.
Thanks for the help. I will try this out and see what the teachers think.
To find out how much farther the minute hand would travel every hour if it were twice as long, we need to calculate the difference in distance traveled between the original minute hand and the new, longer minute hand.
The distance traveled by the minute hand is equivalent to the circumference of the clock face. The formula for the circumference of a circle is C = π * d, where C represents the circumference and d represents the diameter.
1. Calculate the circumference of the original clock face:
- The given diameter of the clock face is 22 feet.
- Using the formula C = π * d, we have C = 3.14 * 22.
- Therefore, the original circumference is approximately 69.08 feet.
2. Calculate the circumference of the new clock face with the longer minute hand (which is twice as long as the original):
- The length of the original minute hand is 12 feet.
- Since the new minute hand is twice as long, its length would be 2 * 12 = 24 feet.
- The diameter of the new clock face is determined by the length of the minute hand plus the original diameter of the clock face. So, the new diameter is 24 + 22 = 46 feet.
- Using the formula C = π * d, we have C = 3.14 * 46.
- Therefore, the new circumference is approximately 144.44 feet.
3. Calculate the difference in distance traveled between the original and new minute hands:
- The difference in distance traveled would be the difference between the new circumference and the original circumference.
- Subtracting the original circumference from the new circumference, we have 144.44 - 69.08 = 75.36 feet.
Therefore, if the minute hand were twice as long, it would travel approximately 75.36 feet farther every hour.