You need to buy a belt that will go around 2 wheels of diameter 4.3 inches. The wheels are 12 inches apart measured from their centers. How long does the belt need to be?  Round your answer to two decimal places

To calculate the length of the belt that goes around two wheels of diameter 4.3 inches, with the wheels being 12 inches apart (measured from their centers), we need to consider two parts: 

1. The length of the belt that goes around half the circumference of each wheel (two semicircles).
2. The length of the belt that spans the straight distance between the two wheels.

### Step 1: Circumference of the wheels
The circumference \( C \) of a circle is calculated by the formula:
\[
C = \pi \times d
\]
where \( d \) is the diameter of the wheel.

For each wheel:
\[
C = \pi \times 4.3 \approx 13.51 \, \text{inches}
\]

Half of this circumference will be:
\[
\frac{C}{2} = \frac{13.51}{2} \approx 6.755 \, \text{inches}
\]

Since there are two wheels, the total length of the belt around the two semicircles is:
\[
2 \times 6.755 = 13.51 \, \text{inches}
\]

### Step 2: Distance between the wheels
The straight sections of the belt span the distance between the centers of the wheels. This distance is given as 12 inches, and since the belt runs along both sides of the wheels, the total straight length of the belt is:
\[
2 \times 12 = 24 \, \text{inches}
\]

### Step 3: Total length of the belt
Now, add the two parts together:
\[
\text{Total belt length} = 13.51 + 24 = 37.51 \, \text{inches}
\]

Thus, the length of the belt should be approximately:
\[
\boxed{37.51} \, \text{inches}
\]

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How would the belt length change if the wheel diameter was increased to 5 inches?
2. What would be the belt length if the distance between the wheel centers increased to 15 inches?
3. How would the solution differ if the wheels had different diameters?
4. What formula can you use for calculating the belt length when the wheels are not aligned horizontally?
5. How does increasing the distance between the centers affect the tension in the belt?

**Tip:** Always remember to account for both the curved and straight sections of the belt when dealing with multiple pulleys or wheels.

You need to buy a belt that will go around 2 wheels of diameter 4.3 inches. The wheels are 12 inches apart measured from their centers. How long does the belt need to be? Round your answer to two decimal places.

Learn how to calculate the length of a belt that goes around two wheels with a 4.3-inch diameter, spaced 12 inches apart. This problem covers key geometry concepts, including the formula for the circumference of a circle and the total belt length formula. Suitable for students in Grades 6-8.

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