To determine how many revolutions a wheel will make, we first need to calculate the distance it covers in one complete revolution, which is the circumference of the wheel. The formula for the circumference of a circle is:

$C = 2\pi r$

where:

• $C$ is the circumference,
• $r$ is the radius of the wheel.

Given:

• Radius $r = 7$ cm,
• Convert the distance the wheel travels into centimeters (since the radius is in cm).

Step 1: Calculate the circumference of the wheel

$C = 2\pi \times 7 = 14\pi \text{ cm}$ Approximating $\pi$ as 3.1416:

$C \approx 14 \times 3.1416 = 43.982 \text{ cm}$

Step 2: Convert the distance the wheel travels into centimeters

Given the distance is 44 kilometers, we convert that to centimeters:

$44 \text{ kilometers} = 44 \times 1000 \times 100 = 4,400,000 \text{ cm}$

Step 3: Calculate the number of revolutions

The number of revolutions is the total distance traveled divided by the circumference of the wheel:

$\text{Revolutions} = \frac{\text{Total distance}}{\text{Circumference}} = \frac{4,400,000}{43.982} \approx 100,000 \text{ revolutions}$

So, the wheel will make approximately 100,000 revolutions to travel 44 kilometers.

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Do you need more details or have any questions?

Here are 5 related questions:

1. How do you calculate the distance traveled in a given number of revolutions?
2. What happens to the number of revolutions if the radius of the wheel is increased?
3. How can we apply this formula to solve for the radius if we know the number of revolutions and the total distance?
4. What is the relationship between the diameter of the wheel and its circumference?
5. How can we use the concept of revolutions in real-world applications, such as in vehicles or machinery?

Tip: When dealing with circular motion problems, always convert units to match the ones used in your calculation to avoid errors.