Math Problem Statement

A bicycle tire has a diameter of 22 in. How many feet does the bicycle travel when the wheel makes 18 revolutions? Round to the nearest hundredth of a foot.

Solution

To find how far the bicycle travels in feet when the wheel makes 18 revolutions, we can use the formula for the circumference of a circle. The circumference of the tire is the distance the wheel covers in one complete revolution.

Step-by-Step Calculation:

  1. Find the circumference of the tire: The formula for the circumference CC of a circle is: C=π×dC = \pi \times d where dd is the diameter. The diameter is given as 22 inches. C=π×223.1416×22=69.115inchesC = \pi \times 22 \approx 3.1416 \times 22 = 69.115 inches

  2. Convert the circumference to feet: Since there are 12 inches in a foot, we convert the circumference from inches to feet: C=69.115125.76 feetC = \frac{69.115}{12} \approx 5.76 \text{ feet}

  3. Find the total distance traveled in 18 revolutions: The bicycle travels a distance equal to the circumference times the number of revolutions: Distance=18×5.76=103.68 feet\text{Distance} = 18 \times 5.76 = 103.68 \text{ feet}

Thus, the bicycle travels approximately 103.68 feet when the wheel makes 18 revolutions.

Do you want more details or have any questions?

Here are 5 related questions:

  1. What is the formula for the area of a circle, and how would you calculate it for the bicycle tire?
  2. How many revolutions would the tire need to travel 1 mile (5280 feet)?
  3. If the diameter of the tire were increased, how would that affect the distance traveled per revolution?
  4. How would the travel distance change if the wheel made 25 revolutions instead of 18?
  5. How many inches does the bicycle travel in one revolution?

Tip: For problems involving circular motion, always start with the circumference to calculate distances.

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Math Problem Analysis

Mathematical Concepts

Geometry
Circle Circumference
Unit Conversion

Formulas

Circumference of a circle: C = π × d
Unit conversion: inches to feet

Theorems

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Suitable Grade Level

Grades 6-8