Pi (π) Math Example 5

Follow the full solution, then compare it with the other examples linked below.

Example 5

hard
A wheel of radius 0.5 m rolls without slipping. How many full rotations does it make to travel 100 m? Use π≈3.14159\pi \approx 3.14159.

Solution

  1. 1
    Step 1: The circumference of the wheel is C=2πr=2×3.14159×0.5≈3.14159C = 2\pi r = 2 \times 3.14159 \times 0.5 \approx 3.14159 m.
  2. 2
    Step 2: Number of rotations =100/3.14159≈31.83= 100 / 3.14159 \approx 31.83.
  3. 3
    Step 3: The number of full rotations is ⌊31.83⌋=31\lfloor 31.83 \rfloor = 31.

Answer

31 full rotations.
Each full rotation moves the wheel forward exactly one circumference. Dividing the total distance by the circumference gives the number of rotations. This principle is used in odometers.

About Pi (π)

The ratio of a circle's circumference to its diameter, approximately 3.14159…3.14159\ldots

Learn more about Pi (π) →

More Pi (π) Examples

Example 1 easy

A circle has a diameter of 10 cm. What is its circumference? Use [formula].

Example 2 medium

A circle has a radius of 7 m. Find its area. Use [formula].

Example 3 medium

A circular pool has a circumference of 31.4 m. Find its radius and area. Use [formula].

Example 4 easy

A circle's circumference is [formula] cm. What is its diameter? Use [formula].

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