How many times the wheel of radius 28 cm must rotate to go 352 m?

Question

Accepted Answer

To determine how many times the wheel of radius 28 cm must rotate to cover a distance of 352 meters, we need to calculate the circumference of the wheel and then find out how many such circumferences fit into the given distance.

1. **Calculate the circumference of the wheel:**
   - The formula for the circumference $ C $ of a circle is given by $ C = 2\pi r $, where $ r $ is the radius.
   - Here, the radius $ r $ is 28 cm.
   - So, the circumference $ C = 2 \times \pi \times 28 $ cm.
   - Approximating $\pi$ as 3.14, we get $ C = 2 \times 3.14 \times 28 = 175.84 $ cm.

2. **Convert the distance from meters to centimeters:**
   - The distance to be covered is 352 meters.
   - Converting meters to centimeters: $ 352 \times 100 = 35200 $ cm.

3. **Calculate the number of rotations:**
   - The number of rotations required is the total distance divided by the circumference of the wheel.
   - Number of rotations = $ \frac{35200}{175.84} \approx 200.16 $.

4. **Round to the nearest whole number:**
   - Since the number of rotations must be a whole number, we round 200.16 to the nearest whole number, which is 200.

Therefore, the wheel must rotate approximately 200 times to cover a distance of 352 meters. This supports Option 1 as the correct answer.

**Explanation for why other options are incorrect:**

- **Option 2 (205):** This option suggests that the wheel would need to rotate 205 times. However, as calculated, the number of rotations required is approximately 200.16, which rounds to 200, not 205. Therefore, this option is incorrect.

- **Option 3 (245):** This option suggests 245 rotations. This is significantly higher than the calculated 200.16 rotations. Thus, it is incorrect.

- **Option 4 (255):** This option suggests 255 rotations. This is even further from the calculated 200.16 rotations, making it incorrect.

In conclusion, based on the calculations and logical reasoning provided, Option 1 is the correct answer.