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)
a) Circumference = π x diameter = 3.14 x 2.5 ft = 7.85 ft
b) 5,280 ft / 7.85 ft = 671.5 rotations
To find the circumference of a tire, we can use the formula:
Circumference (C) = π × Diameter (d)
Given that the diameter of the tire is 2.5 ft:
Circumference (C) = π × 2.5 ft
Now let's calculate the circumference:
Circumference (C) = 3.14159 × 2.5 ft
Circumference (C) ≈ 7.85398 ft
So, the circumference of the tire is approximately 7.85398 ft.
To find out how many times the tire will have to rotate to travel 1 mile (5,280 ft), we can divide the distance traveled by the circumference of the tire:
Number of rotations = Distance traveled / Circumference
Number of rotations = 5,280 ft / 7.85398 ft
Now let's calculate the number of rotations:
Number of rotations ≈ 672
Therefore, the tire will have to rotate approximately 672 times to travel a distance of 1 mile.
To find the circumference of the tire, we can use the formula:
Circumference = π * Diameter
Given the diameter of the tire is 2.5 ft, we can substitute this value into the formula:
Circumference = π * 2.5 ft
Now, to find the approximate number of times the tire will have to rotate to travel 1 mile, we need to divide the distance traveled (1 mile = 5,280 ft) by the circumference of the tire.
Approximate number of rotations = Distance traveled / Circumference
Now let's calculate both parts step by step.
Part a: Finding the circumference of the tire
Circumference = π * Diameter
Circumference = 3.14 * 2.5 ft
Circumference ≈ 7.85 ft (rounded to two decimal places)
Therefore, the circumference of the tire is approximately 7.85 ft.
Part b: Finding the approximate number of rotations to travel 1 mile
Approximate number of rotations = Distance traveled / Circumference
Approximate number of rotations = 5280 ft / 7.85 ft
Approximate number of rotations ≈ 672.73 rotations (rounded to two decimal places)
Therefore, the tire will have to rotate approximately 672.73 times to travel 1 mile.