A wheel has a radius of 35 cm. How many revolution will it make to cover 11 km ?

Question

Accepted Answer

To determine how many revolutions a wheel with a radius of 35 cm will make to cover a distance of 11 km, we need to follow these steps:

1. **Calculate the Circumference of the Wheel:**
   The circumference $ C $ of a circle (or wheel) is given by the formula:
   $$
   C = 2 \pi r
   $$
   where $ r $ is the radius of the wheel. For this wheel, $ r = 35 $ cm.
   $$
   C = 2 \times \pi \times 35 \approx 2 \times 3.1416 \times 35 \approx 219.91 \text{ cm}
   $$

2. **Convert the Distance from Kilometers to Centimeters:**
   Since the circumference is in centimeters, we need to convert the distance from kilometers to centimeters. 
   $$
   11 \text{ km} = 11 \times 1000 \times 100 = 1,100,000 \text{ cm}
   $$

3. **Calculate the Number of Revolutions:**
   The number of revolutions $ N $ is the total distance divided by the circumference of the wheel.
   $$
   N = \frac{\text{Total Distance}}{\text{Circumference}} = \frac{1,100,000}{219.91} \approx 5000
   $$

Thus, the wheel will make approximately 5000 revolutions to cover 11 km, which corresponds to Option 3.

**Explanation for Other Options:**

- **Option 1 (4800):** This option underestimates the number of revolutions. Given the calculations, 4800 revolutions would not cover the full 11 km distance.
  
- **Option 2 (4990):** This option is very close but still slightly underestimates the number of revolutions needed. The precise calculation shows that 5000 is the correct number.

- **Option 4 (5020):** This option overestimates the number of revolutions. The calculation clearly shows that 5000 revolutions are sufficient to cover the 11 km distance.

In conclusion, based on the calculations, Option 3 (5000 revolutions) is indeed the correct answer.