How many times a wheel of diameter 105 cm will rotate to covering a distance of 330 m?

Options

A. 100 revolutions
B. 110 revolutions
C. 90 revolutions
D. 105 revolutions

Answer

To find out how many times a wheel of diameter 105 cm will rotate to cover a distance of 330 m, we can follow these steps:

### Step 1: Convert the distance from meters to centimeters
Since the diameter is given in centimeters, we need to convert the distance from meters to centimeters.
- Distance to cover = 330 m = 330 × 100 cm = 33000 cm.

**Hint:** Remember that 1 meter = 100 centimeters.

### Step 2: Calculate the radius of the wheel
The radius is half of the diameter.
- Diameter = 105 cm
- Radius = Diameter / 2 = 105 cm / 2 = 52.5 cm.

**Hint:** The radius is always half of the diameter.

### Step 3: Calculate the circumference of the wheel
The circumference (C) of a circle is given by the formula:
\[ C = 2 \pi r \]
Using \( \pi \approx \frac{22}{7} \):
- Circumference = \( 2 \times \frac{22}{7} \times 52.5 \).

Calculating this:
- Circumference = \( 2 \times \frac{22}{7} \times 52.5 = \frac{44 \times 52.5}{7} \).
- Circumference = \( \frac{2310}{7} = 330 \) cm.

**Hint:** The circumference tells you how far the wheel travels in one complete rotation.

### Step 4: Calculate the number of rotations
To find the number of rotations (N), we can use the formula:
\[ N = \frac{\text{Distance}}{\text{Circumference}} \]
Substituting the values we have:
- \( N = \frac{33000 \text{ cm}}{330 \text{ cm}} = 100 \).

**Hint:** The number of rotations is found by dividing the total distance by the circumference of the wheel.

### Conclusion
The wheel will rotate **100 times** to cover a distance of 330 m.

**Final Answer:** 100 revolutions.