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)
please show me how to put all the work necessary if not my teacher will give me a bad grade!!
a) To find the circumference of the tire, we use the formula:
Circumference = π x diameter
where π is a constant equal to approximately 3.14.
Substituting the given diameter of 2.5 ft, we get:
Circumference = π x 2.5 ft
Circumference = 7.85 ft (rounded to two decimal places)
Therefore, the circumference of the tire is approximately 7.85 ft.
b) To find how many times the tire will have to rotate to travel 1 mile, we need to first find how many times it will rotate to travel 1 ft (since 1 mile = 5,280 ft).
The distance traveled by one rotation of the tire is equal to its circumference. From part a, we know that the circumference is 7.85 ft.
Therefore, the number of times the tire will rotate to travel 1 ft is:
1 ft ÷ 7.85 ft/rotation ≈ 0.127 rotations
(Note: We rounded to three decimal places.)
To find how many times it will rotate to travel 1 mile, we multiply by the number of feet in a mile:
0.127 rotations/ft x 5,280 ft/mile ≈ 670 rotations
Therefore, the tire will have to rotate approximately 670 times to travel 1 mile.
thx
You're welcome! Don't hesitate to ask if you have any other questions.
Sure, I'll guide you step-by-step on how to solve these problems.
a) Finding the circumference of the tire:
The formula to find the circumference of a circle is C = πd, where C represents the circumference and d is the diameter. Given that the diameter of the tire is 2.5 ft, we can substitute this value into the formula.
C = π * 2.5
C ≈ 7.85 ft
So, the circumference of the tire is approximately 7.85 ft.
b) Finding the number of rotations to travel 1 mile:
To find the number of rotations required to travel a certain distance, we need to divide the distance traveled by the circumference of the tire.
1 mile is equal to 5,280 ft, as stated in the question. Now, we can use this value along with the previously calculated circumference.
Number of rotations = Distance traveled / Circumference
Number of rotations = 5280 ft / 7.85 ft
Number of rotations ≈ 672.61 rotations
Therefore, the tire will have to rotate approximately 672.61 times to travel 1 mile.
Remember to round your final answers appropriately, as mentioned in the question.