How many feet does a wheel with a diameter of 20 inches travel after one, five, and 30 revolutions?
for one ... 20 π / 12
multiply to get five and thirty
To find the distance a wheel travels after a certain number of revolutions, you need to know the circumference of the wheel. The circumference is equal to the distance traveled in one complete revolution.
The formula to calculate the circumference of a wheel is:
Circumference = π * Diameter
Since you're given the diameter of the wheel as 20 inches, you can calculate the circumference as follows:
Circumference = π * 20 inches
Now, let's calculate the circumference using the value of π as 3.14159:
Circumference = 3.14159 * 20 inches
Circumference = 62.8318 inches
After finding the circumference, you can determine the distance the wheel travels by multiplying the circumference by the number of revolutions.
For one revolution:
Distance = Circumference * 1
Distance = 62.8318 inches * 1
Distance = 62.8318 inches
After five revolutions:
Distance = Circumference * 5
Distance = 62.8318 inches * 5
Distance = 314.159 inches
After thirty revolutions:
Distance = Circumference * 30
Distance = 62.8318 inches * 30
Distance = 1,884.954 inches
To convert these distances from inches to feet, divide each distance by 12 inches (since there are 12 inches in a foot):
For one revolution:
Distance = 62.8318 inches / 12 inches per foot
Distance ≈ 5.2368 feet
After five revolutions:
Distance = 314.159 inches / 12 inches per foot
Distance ≈ 26.1799 feet
After thirty revolutions:
Distance = 1,884.954 inches / 12 inches per foot
Distance ≈ 157.0795 feet
Therefore, a wheel with a diameter of 20 inches would travel approximately 5.2368 feet, 26.1799 feet, and 157.0795 feet after one, five, and thirty revolutions, respectively.