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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)
AAAaannndd the bot gets it wrong yet again!
C=Οd
so cut the circumference by half, and double the rotations needed.
To find the circumference of the tire, we can use the formula:
Circumference = Ο * diameter
Part a:
Given that the diameter of the tire is 2.5 ft, we can substitute this value into the formula:
Circumference = Ο * 2.5 ft
Using an approximate value of Ο = 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 β 672
Therefore, the tire will have to rotate approximately 672 times to travel 1 mile.
To find the circumference of the tire, we can use the formula:
Circumference = Ο x Diameter
Given that the diameter of the tire is 2.5 ft, we can substitute this value into the formula:
Circumference = Ο x 2.5 ft
Now, we need to calculate the circumference using the value of Ο. Let's assume Ο as approximately 3.14:
Circumference β 3.14 x 2.5 ft
Circumference β 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 β 671.97
Therefore, the tire will have to rotate approximately 671.97 times to travel 1 mile.
a) Circumference = 2Οr
= 2Ο(2.5 ft)
= 5Ο ft
b) Circumference of tire = 5Ο ft
Distance traveled in 1 rotation = 5Ο ft
Number of rotations to travel 1 mile = 5,280 ft / 5Ο ft
= 1056/Ο rotations
β 333.5 rotations