A car with a 65cm diameter wheel travels 3.0km. How many revolutions does the wheel make in this distance?
find the circumference
C = pi D = pi * 0.65 meters per revolution
C * n = 3,000 meters
so
n = 3,000/C
To determine how many revolutions the wheel makes, we need to find out how many times the circumference of the wheel fits into the distance traveled.
First, we need to find the circumference of the wheel. The formula for the circumference of a circle is C = π * d, where C is the circumference and d is the diameter.
Given that the diameter of the wheel is 65cm, we can calculate the circumference as follows:
C = π * 65cm
Using the value of π (pi) as approximately 3.14, we have:
C ≈ 3.14 * 65cm
C ≈ 204.1cm
Now that we know the circumference of the wheel, we can find out how many times it fits into the distance traveled.
The distance traveled is 3.0km, but we need to convert it into centimeters to match the units with the circumference. There are 100 centimeters in 1 meter and 1000 meters in 1 kilometer, so:
3.0km = 3,000m = 3,000 * 100cm
3.0km = 300,000cm
Now we can calculate the number of revolutions by dividing the distance traveled by the circumference:
Number of revolutions = distance traveled / circumference
Number of revolutions = 300,000cm / 204.1cm
Number of revolutions ≈ 1,470.4
Therefore, the wheel would make approximately 1,470.4 revolutions in this distance.