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:
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Find the circumference of the tire: The formula for the circumference of a circle is: where is the diameter. The diameter is given as 22 inches.
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Convert the circumference to feet: Since there are 12 inches in a foot, we convert the circumference from inches to feet:
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Find the total distance traveled in 18 revolutions: The bicycle travels a distance equal to the circumference times the number of revolutions:
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:
- What is the formula for the area of a circle, and how would you calculate it for the bicycle tire?
- How many revolutions would the tire need to travel 1 mile (5280 feet)?
- If the diameter of the tire were increased, how would that affect the distance traveled per revolution?
- How would the travel distance change if the wheel made 25 revolutions instead of 18?
- 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
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