Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
The diameter of a tire is 2.5 ft. Use this measurement to answer parts a and b. Show all work to receive full credit.
Find the circumference of the tire.
About how many times will the tire have to rotate to travel 1 mile? (1 mile = 5,280 ft)
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A bicycle has a radius of 14 inches. What is the circumference of the tire?
Explain the steps needed to solve this problem.
To find the circumference of the tire, we use the formula:
Circumference = π * diameter
Given that the diameter of the tire is 2.5 ft, we can substitute this value into the formula:
Circumference = π * 2.5 ft
Now, let's calculate the circumference.
To find the circumference, we need to know the value of π (pi). Pi is an irrational number, commonly approximated to 3.14 or 22/7.
So, let's calculate the circumference using two different approximations: 3.14 and 22/7.
1) Using π = 3.14:
Circumference = 3.14 * 2.5 ft
Circumference = 7.85 ft
2) Using π = 22/7:
Circumference = (22/7) * 2.5 ft
Circumference = 7.85 ft
Hence, the circumference of the tire is approximately 7.85 ft.
Now, let's calculate how many times the tire will have to rotate to travel 1 mile (5,280 ft).
To find the number of rotations, we can use the formula:
Number of rotations = Distance traveled / Circumference
Given that the distance traveled is 1 mile (5,280 ft), we can substitute this value into the formula:
Number of rotations = 5,280 ft / 7.85 ft
Let's calculate the number of rotations.
Number of rotations ≈ 672.61
Therefore, the tire will rotate approximately 672.61 times to travel 1 mile.
C = πd
5280/C = ___