To find the radius of the tires in inches, we need to use the following relationship between distance, circumference, and revolutions:
Circumference = 2πr
where:
- Circumference is the distance traveled in one revolution of the tire.
- "r" is the radius of the tire.
In this case, you know that the car travels 3 miles, and its tires make 2600 revolutions. You want to find the radius in inches.
First, convert the distance traveled from miles to inches because the radius will be in inches:
1 mile = 63,360 inches (since 1 mile = 5,280 feet, and 1 foot = 12 inches)
So, 3 miles = 3 * 63,360 inches = 190,080 inches
Now, you can use the relationship between distance, circumference, and revolutions:
Circumference = Distance / Revolutions
Circumference = 190,080 inches / 2600 revolutions
Now, you can calculate the circumference of the tire in inches per revolution:
Circumference = 190,080 inches / 2600 revolutions ≈ 73.1 inches per revolution
Now, you know the circumference of the tire, and you can use it to find the radius (r):
73.1 inches = 2πr
Divide both sides by 2π to isolate "r":
r ≈ 73.1 inches / (2π) ≈ 11.64 inches (rounded to two decimal places)
Answer
So, the radius of the tires is approximately 11.64 inches.