a tires diameter is 10 inches and the circumference is 31 inches, how many times will the tire rotate in 10,000 miles, show all calculations
To find the number of times the tire will rotate in 10,000 miles, we need to determine the distance traveled by the tire in one full rotation and then divide 10,000 miles by that distance.
Since the tire's diameter is given as 10 inches, we can find its radius by dividing the diameter by 2: 10 inches / 2 = 5 inches.
The circumference of a circle is calculated using the formula: C = 2πr, where C is the circumference and r is the radius.
So, the circumference of the tire can be calculated as follows: C = 2 * π * r = 2 * 3.14159 * 5 = 31.4159 inches (approximately).
Next, we need to calculate the number of rotations in one mile by dividing the total distance traveled in each mile by the circumference of the tire: 1 mile / 31.4159 inches = 0.0318309886 rotations per mile (approximately).
To find the number of rotations in 10,000 miles, we multiply the rotations per mile by the total number of miles: 0.0318309886 rotations/mile * 10,000 miles = 318.309886 rotations (approximately).
Therefore, the tire will rotate approximately 318.309886 times in 10,000 miles.
redo the calculations using 31 inches as the circumference
If the circumference of the tire is 31 inches, then we can calculate the radius using the formula for circumference:
C = 2πr
Rearranging the formula to solve for the radius:
r = C / (2π) = 31 inches / (2 * 3.14159) = 4.9367 inches (approximately).
Now, we can calculate the distance traveled in one full rotation of the tire based on its circumference:
Distance traveled in one rotation = Circumference = 31 inches.
To find the number of rotations in 10,000 miles, we need to convert the distance traveled to miles:
Distance traveled in one mile = 5280 feet (since 1 mile = 5280 feet).
Converting this distance to inches:
Distance traveled in one mile = 5280 feet * 12 inches/feet = 63,360 inches.
To find the number of rotations in 10,000 miles, we divide the total distance by the distance traveled in one full rotation:
Number of rotations in 10,000 miles = 10,000 miles * (63,360 inches / 31 inches) = 20,322,580.6 rotations (approximately).
Therefore, the tire will rotate approximately 20,322,580.6 times in 10,000 miles.