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Question

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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)

Answer 1

AAAaannndd the bot gets it wrong yet again!

C=πd
so cut the circumference by half, and double the rotations needed.

Answer 2

To find the circumference of the tire, we can use the formula:

Circumference = π * diameter

Part a:

Given that the diameter of the tire is 2.5 ft, we can substitute this value into the formula:

Circumference = π * 2.5 ft

Using an approximate value of π = 3.14, we can calculate the circumference:

Circumference = 3.14 * 2.5 ft
Circumference = 7.85 ft

Therefore, the circumference of the tire is 7.85 ft.

Part b:

To find out how many times the tire will have to rotate to travel 1 mile (5,280 ft), we need to divide the distance travelled by the circumference of the tire.

Distance travelled = 1 mile = 5,280 ft

Number of rotations = Distance travelled / Circumference

Number of rotations = 5,280 ft / 7.85 ft
Number of rotations ≈ 672

Therefore, the tire will have to rotate approximately 672 times to travel 1 mile.

Answer 3

To find the circumference of the tire, we can use the formula:

Circumference = π x Diameter

Given that the diameter of the tire is 2.5 ft, we can substitute this value into the formula:

Circumference = π x 2.5 ft

Now, we need to calculate the circumference using the value of π. Let's assume π as approximately 3.14:

Circumference ≈ 3.14 x 2.5 ft
Circumference ≈ 7.85 ft

Therefore, the circumference of the tire is approximately 7.85 ft.

Now, let's move on to part b to determine how many times the tire will have to rotate to travel 1 mile.

Since 1 mile equals 5,280 ft, we need to find out how many times the tire's circumference fits into 5,280 ft.

Number of rotations = Distance / Circumference

Number of rotations = 5,280 ft / 7.85 ft

Now, let's divide to find the answer:

Number of rotations ≈ 671.97

Therefore, the tire will have to rotate approximately 671.97 times to travel 1 mile.

Answer 4

a) Circumference = 2πr

= 2π(2.5 ft)
= 5π ft

b) Circumference of tire = 5π ft
Distance traveled in 1 rotation = 5π ft
Number of rotations to travel 1 mile = 5,280 ft / 5π ft
= 1056/π rotations
≈ 333.5 rotations