The centers of 2 wheels are horizontally 36 cm apart. The diameter of the larger wheel is 15 cm and the diameter of the smaller wheel is 6 cm. Find the actual distance between the centers of the two wheels. In other words, find the distance from A to B. Round your answer to two decimal places. Include the units. (For example, 12.34 cm.)

We are given two wheels, with their centers horizontally 36 cm apart, and the diameters of the wheels are 15 cm and 6 cm, respectively.

### Step-by-step breakdown:

1. **Identify the radii of the wheels:**
   - The radius of the larger wheel is half of its diameter:
     \[
     r_{\text{large}} = \frac{15}{2} = 7.5 \, \text{cm}
     \]
   - The radius of the smaller wheel is half of its diameter:
     \[
     r_{\text{small}} = \frac{6}{2} = 3 \, \text{cm}
     \]

2. **Vertical distance between the centers of the two wheels:**
   - The vertical distance between the centers is the difference between the radii of the two wheels:
     \[
     \text{Vertical distance} = 7.5 - 3 = 4.5 \, \text{cm}
     \]

3. **Actual distance between the centers:**
   The centers of the two wheels form a right triangle where the horizontal distance is the base, the vertical distance is the height, and the actual distance is the hypotenuse.

   Using the Pythagorean theorem:
   \[
   \text{Distance} = \sqrt{(36^2 + 4.5^2)} = \sqrt{(1296 + 20.25)} = \sqrt{1316.25}
   \]
   \[
   \text{Distance} \approx 36.28 \, \text{cm}
   \]

So, the actual distance between the centers of the two wheels is approximately **36.28 cm**.

Would you like a detailed explanation on any of the steps?

Here are 5 questions to expand on the concept:
1. What is the Pythagorean theorem and how does it apply to this problem?
2. How would the problem change if the distance between the wheel centers was vertical instead of horizontal?
3. Can you apply this concept to find distances between centers of circular objects in other situations?
4. What would the distance be if the diameters of the wheels were swapped?
5. How does changing the size of either wheel affect the overall distance?

**Tip:** Always remember to halve the diameter to find the radius when dealing with circular objects!

The centers of 2 wheels are horizontally 36 cm apart. The diameter of the larger wheel is 15 cm and the diameter of the smaller wheel is 6 cm. Find the actual distance between the centers of the two wheels. Round your answer to two decimal places.

Learn how to calculate the actual distance between the centers of two wheels with diameters of 15 cm and 6 cm, placed 36 cm apart horizontally. This step-by-step solution applies the Pythagorean Theorem to solve the problem. Suitable for students in Grades 6-8.

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