A car's wheels are 24 in. in diameter. How far (in mi) will the car travel if its wheels revolve 10,000 times without slipping? (Round your answer to two decimal places).

To determine how far the car travels, we first need to calculate the circumference of the car's wheels. The circumference of a circle can be found using the formula:

\[
C = \pi \times d
\]

where \( C \) is the circumference and \( d \) is the diameter.

Given:
- Diameter of the wheel, \( d = 24 \) inches
- Number of revolutions, \( n = 10,000 \)

1. **Calculate the circumference of the wheel:**

\[
C = \pi \times 24 \text{ inches}
\]

\[
C \approx 3.1416 \times 24
\]

\[
C \approx 75.3984 \text{ inches}
\]

2. **Calculate the total distance traveled in inches:**

Since the car's wheels revolve 10,000 times, the total distance traveled is the number of revolutions multiplied by the circumference of the wheel:

\[
\text{Total distance} = n \times C
\]

\[
\text{Total distance} = 10,000 \times 75.3984 \text{ inches}
\]

\[
\text{Total distance} \approx 753,984 \text{ inches}
\]

3. **Convert the total distance from inches to miles:**

There are 63,360 inches in a mile. So, to convert the distance from inches to miles:

\[
\text{Total distance in miles} = \frac{753,984}{63,360}
\]

\[
\text{Total distance in miles} \approx 11.9 \text{ miles}
\]

Therefore, the car will travel approximately **11.90 miles** if its wheels revolve 10,000 times without slipping.

Would you like more details or have any questions?

Here are 5 related questions that expand upon this information:

1. How far would the car travel if the diameter of the wheels were 30 inches and still revolved 10,000 times?
2. How many revolutions would the wheels need to make for the car to travel exactly 50 miles?
3. If a car travels 100 miles, how many times would its 24-inch diameter wheels revolve?
4. How would the distance change if the wheels were 18 inches in diameter and revolved 10,000 times?
5. What is the relationship between the diameter of a wheel and the number of revolutions needed to travel a specific distance?

**Tip:** Remember, to find the distance traveled by any rolling object, you can always multiply the circumference of the wheel by the number of revolutions.

Discover how far a car travels when its 24-inch wheels revolve 10,000 times. Learn the formula for circumference of a circle and how it applies to this problem. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation