A bicycle has a rear wheel with a diameter of 26 inches.

How far does the bicycle travel forward if the rear wheel rotates through an angle of 135°?

To determine how far the bicycle travels forward when the rear wheel rotates through an angle of 135°, we need to follow these steps:

### Step 1: Calculate the Circumference of the Wheel
The circumference of the wheel is the distance the bicycle travels in one full rotation of the wheel. The circumference \( C \) of a circle is given by the formula:
\[
C = \pi \times d
\]
where \( d \) is the diameter of the wheel.

Given:
\[
d = 26 \text{ inches}
\]
\[
C = \pi \times 26 \approx 81.68 \text{ inches}
\]

### Step 2: Determine the Fraction of the Rotation
The angle of rotation is 135°, which is a fraction of a full rotation (360°). The fraction of the full rotation is:
\[
\text{Fraction} = \frac{135^\circ}{360^\circ} = \frac{3}{8}
\]

### Step 3: Calculate the Distance Traveled
The distance traveled \( D \) is the fraction of the circumference corresponding to the angle of rotation:
\[
D = \text{Fraction} \times C = \frac{3}{8} \times 81.68 \text{ inches}
\]
\[
D \approx 30.63 \text{ inches}
\]

### Conclusion:
The bicycle travels approximately **30.63 inches** forward when the rear wheel rotates through an angle of 135°.

Would you like more details or have any questions about this calculation?

Here are 5 related questions for further exploration:

1. How far does the bicycle travel if the rear wheel rotates through a full 360°?
2. What is the travel distance if the wheel rotates through a 90° angle?
3. How would the travel distance change if the wheel diameter were 28 inches instead of 26 inches?
4. What is the angle of rotation if the bicycle needs to travel exactly 50 inches?
5. How many complete rotations does the wheel make if the bicycle travels 1 mile?

**Tip:** Remember, the distance traveled by the wheel is directly proportional to the angle of rotation.

Explore how to calculate the distance traveled by a bicycle when its rear wheel with a diameter of 26 inches rotates 135°. This problem involves using the circumference formula and understanding fractions of rotation. Suitable for Grades 7-9.

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