Question
A car travels 2000π feet when the diameter of the wheel is 4 feet. How many revolutions were made?
Answers
GPT-4o mini
To find out how many revolutions the car's wheel made, we first need to determine the circumference of the wheel. The formula for the circumference \( C \) of a circle is given by:
\[
C = \pi \times d
\]
where \( d \) is the diameter of the circle. In this case, the diameter of the wheel is 4 feet, so we can calculate the circumference as follows:
\[
C = \pi \times 4 = 4\pi \text{ feet}
\]
Next, we want to find out how many revolutions the wheel makes when the car travels a distance of \( 2000\pi \) feet. The number of revolutions \( N \) can be calculated by dividing the total distance traveled by the circumference of the wheel:
\[
N = \frac{\text{Total distance traveled}}{\text{Circumference of the wheel}} = \frac{2000\pi}{4\pi}
\]
Now, simplifying this expression:
\[
N = \frac{2000\pi}{4\pi} = \frac{2000}{4} = 500
\]
Thus, the number of revolutions made by the wheel is:
\[
\boxed{500}
\]
\[
C = \pi \times d
\]
where \( d \) is the diameter of the circle. In this case, the diameter of the wheel is 4 feet, so we can calculate the circumference as follows:
\[
C = \pi \times 4 = 4\pi \text{ feet}
\]
Next, we want to find out how many revolutions the wheel makes when the car travels a distance of \( 2000\pi \) feet. The number of revolutions \( N \) can be calculated by dividing the total distance traveled by the circumference of the wheel:
\[
N = \frac{\text{Total distance traveled}}{\text{Circumference of the wheel}} = \frac{2000\pi}{4\pi}
\]
Now, simplifying this expression:
\[
N = \frac{2000\pi}{4\pi} = \frac{2000}{4} = 500
\]
Thus, the number of revolutions made by the wheel is:
\[
\boxed{500}
\]