Final answer:
To find the radius of a tire given that a car travels 3 miles with 2640 revolutions, you can calculate the circumference of the tire using the distance and revolutions and then solve for the radius. The radius is approximately 11.46 inches.
Step-by-step explanation:
The student is asking for the radius of a car tire given the distance the car travels and the number of tire revolutions. To find the tire radius, we have to relate the distance traveled with the circumference of the tire, which involves solving for the radius in the formula for the circumference of a circle.
First, convert the distance traveled into inches:
3 miles = 3 x 5280 feet x 12 inches/foot = 190080 inches.
Then, use the relationship between the distance traveled and the number of revolutions (number of times the circumference of the tire rolled on the ground) to find the circumference of the tire:
Circumference = Total distance / Number of revolutions = 190080 inches / 2640 revolutions = 72 inches.
Finally, solve for the radius using the formula for circumference C = 2 π r:
C = 72 inches = 2 π r
r = 72 inches / (2 π)
r ≈ 11.46 inches
So, the radius of the tire is approximately 11.46 inches.