Question

If a bicycle has a wheel radius of 14 inches, what is the distance covered by the bicycle when the wheel makes 10 complete rotations?

Answer 1

To solve this problem, let's break it down into steps and translate the narrative into a mathematical equation:

Understanding the Problem:

• We have a bicycle with a wheel radius of 14 inches.
• We need to find the distance covered by the bicycle when the wheel makes 10 complete rotations.

Translating to a Mathematical Equation

1. Find the Circumference of the Wheel: The distance covered in one rotation of the wheel equals the circumference of the wheel. The circumference
`C` of a circle (wheel) is calculated using the formula:
`C=2\pi r`, where
`r` is the radius of the circle.

2. Calculate Total Distance: The total distance covered by 10 rotations is 10 times the circumference.

Steps to Solve

1. Calculate the Circumference:

Using the formula
`C=2\pi r`, with
`r=14` inches, we get:

`C=2*3.1416*14\approx87.96` inches

2. Calculate Total Distance:

The total distance is the circumference multiplied by the number of rotations

Total distance = Circumference × Number of Rotations

Total distance =
`87.9646` inches × 10 ≈ 879.65 inches.

Therefore, the bicycle covers approximately 879.65 inches when its wheel makes 10 complete rotations.