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The problem involves two gears that are connected and rotate together. The smaller gear has a radius of 3.3 cm, and the larger gear has a radius of 7.1 cm. We are given that the smaller gear rotates through an angle of 300°, and we need to calculate how many degrees the larger gear rotates.

### Step-by-Step Solution:

1. **Gear Rotation and Radii:**
   - When gears are connected, the number of teeth or the circumference (proportional to the radius) determines the relative number of rotations.
   - The angle of rotation of the larger gear is inversely proportional to the ratio of the radii of the gears because the same length of teeth (arc length) is covered by both gears.

2. **Ratio of Radii:**
   - The ratio of the radii of the smaller gear to the larger gear is:
   \[
   \text{Ratio} = \frac{\text{Radius of smaller gear}}{\text{Radius of larger gear}} = \frac{3.3}{7.1}
   \]

3. **Relation of Rotations:**
   - Since the larger gear rotates more slowly than the smaller gear, the angle through which the larger gear rotates is reduced by this ratio:
   \[
   \text{Angle of larger gear} = \text{Angle of smaller gear} \times \frac{\text{Radius of smaller gear}}{\text{Radius of larger gear}} = 300^\circ \times \frac{3.3}{7.1}
   \]

Let's calculate this.The larger gear will rotate through approximately **139.44°** when the smaller gear rotates through 300°.

Would you like more details or have any further questions?

Here are 5 related questions to explore:

1. What would happen if the radii of both gears were equal?
2. How would the answer change if the smaller gear rotated through 500° instead of 300°?
3. What is the relationship between gear size and rotational speed?
4. How many full rotations will the smaller gear make for the larger one to complete a full rotation?
5. How can we apply the gear rotation concept to real-world machinery like clocks or bikes?

**Tip:** The angle of rotation for interconnected gears is always inversely proportional to their radius ratio. This can help in mechanical design and understanding torque relationships.

Two gears are adjusted so that the smaller gear drives the larger one, as shown in the figure. If the smaller gear rotates through an angle of 300°, through how many degrees will the larger gear rotate?

Learn how to solve a gear rotation problem involving two gears with different radii. The smaller gear rotates 300°, and you calculate the rotation of the larger gear based on the radius ratio. This solution includes key geometric concepts and is suitable for high school students.

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