Find out how many times the back wheel spins: If a bike's front wheel goes around 230 times because it has a circumference of 77, how many times will the back wheel spin, which has a circumference of 55?

If a cycle has front wheel of perimeter 77 and back wheel of 55. If front wheel revolves 230 times. How many revolutions will the back wheel take?

The back wheel will make 322 revolutions.

Here's how

To solve this problem, we can use the concept that the distance traveled by each wheel in one revolution is equal to its perimeter.

For the front wheel:

Perimeter of the front wheel = 77 units

Number of revolutions of the front wheel = 230

So, the total distance traveled by the front wheel

= Perimeter × Number of revolutions

= 77 × 230

= 17710 units

Now, since both wheels travel the same distance in one revolution, we can find the number of revolutions for the back wheel by dividing the total distance traveled by the back wheel's perimeter:

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Number of revolutions of the back wheel = Total distance traveled by the front wheel / Perimeter of the back wheel

= 17710 units / 55 units ≈ 321.818181...

Therefore, the back wheel will make approximately 322 revolutions.

Circumference of a Circle

The circumference of a circle is the total distance around its edge. It's essentially the length of a line that perfectly follows the circle's curve. There are two main ways to calculate the circumference, depending on what information you have about the circle:

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1. Using the radius:

  • Formula: Circumference = 2πr, where:
    • π (pi) is a mathematical constant approximately equal to 3.14159 (you can use 3.14 for most basic calculations).
    • r is the radius of the circle, which is the distance from the center to any point on the edge.

2. Using the diameter:

  • Formula: Circumference = πd, where:
    • π (pi) is the same mathematical constant as above.
    • d is the diameter of the circle, which is the distance across the circle through its center (essentially, twice the radius).