An automobile with 0.310 m radius tires travels 85,000 km before wearing them out. How many revolutions do the tires make, neglecting any backing up and any change in radius due to wear?
Circumference = pi * 2r = 3.14 * 0.620 =
1.95 m/rev.
8.5*10^7m * 1rev/1.95m = 4.36*10^7 Revs
= 43.6 Million Revs.
Well, let's calculate this in a fun and goofy way!
To find the number of revolutions, we need to calculate the total distance traveled by the car and then divide it by the circumference of the tire.
First, let's find the total distance traveled in meters:
85,000 km = 85,000,000 meters
Now, to find the circumference of the tire, we can use the formula:
Circumference = 2 * π * radius
Circumference = 2 * 3.14159 * 0.310 m
Circumference ≈ 1.94375 m
Now, let's divide the total distance traveled by the circumference of the tire:
Number of revolutions = 85,000,000 m / 1.94375 m ≈ 43,735,181 revolutions
So, the tires make approximately 43,735,181 revolutions before wearing out. And believe me, those tires sure know how to spin!
To find the number of revolutions the tires make, we need to calculate the distance traveled in terms of circumference of the tires.
Step 1: Calculate the circumference of the tires.
The circumference of a circle can be calculated using the formula: C = 2πr, where C is the circumference and r is the radius.
Given that the radius of the tires is 0.310 m, we can substitute this value into the formula.
C = 2π(0.310) = 1.946 m
Step 2: Calculate the distance traveled by the automobile in meters.
The question states that the automobile travels 85,000 km. We need to convert this distance into meters.
1 km = 1000 m. Therefore, 85,000 km = 85,000 x 1000 = 85,000,000 m.
Step 3: Calculate the number of revolutions.
To find the number of revolutions, we need to divide the total distance traveled by the circumference of the tires.
Number of revolutions = Total distance / Circumference of the tires = 85,000,000 m / 1.946 m = 43,719,806 revolutions.
Therefore, the tires make approximately 43,719,806 revolutions before wearing out, neglecting any backing up and any change in radius due to wear.
To calculate the number of revolutions made by the tires, we need to know the distance covered by each revolution.
The circumference of a circle is given by the formula:
Circumference = 2πr,
where r is the radius of the circle.
In this case, the radius of the tires is given as 0.310 m. Therefore, the distance covered by each revolution can be calculated as follows:
Distance per revolution = Circumference of tire = 2π(0.310) = 1.947 meters.
Now, we know that the automobile has traveled 85,000 km, but the distance per revolution is in meters. So, we need to convert the distance traveled by the automobile from kilometers to meters.
1 kilometer = 1000 meters. Therefore, 85,000 kilometers = 85,000 * 1000 = 85,000,000 meters.
Finally, to find the number of revolutions, we can divide the total distance traveled by the distance covered per revolution:
Number of revolutions = Total distance traveled / Distance per revolution
= 85,000,000 meters / 1.947 meters
≈ 43,696,087 revolutions.
So, the tires of the automobile make approximately 43,696,087 revolutions before wearing out.