The wheel of a motorcycle is of radius 35 cm .How many revolutions are required to travel a distance of 11 m ?

Answer

To find out how many revolutions are required for a motorcycle wheel with a radius of 35 cm to travel a distance of 11 meters, we can follow these steps:

### Step 1: Convert the distance from meters to centimeters
Since the radius is given in centimeters, we should convert the distance into the same unit.

\[ \text{Distance in cm} = 11 \text{ m} \times 100 \text{ cm/m} = 1100 \text{ cm} \]

### Step 2: Calculate the circumference of the wheel
The circumference (C) of a circle (which is the distance covered in one complete revolution) is calculated using the formula:

\[ C = 2 \pi r \]

Substituting the radius (r = 35 cm):

\[ C = 2 \times \pi \times 35 \]

Using \(\pi \approx \frac{22}{7}\):

\[ C = 2 \times \frac{22}{7} \times 35 \]

Calculating this gives:

\[ C = \frac{2 \times 22 \times 35}{7} = \frac{1540}{7} \approx 220 \text{ cm} \]

### Step 3: Calculate the number of revolutions
To find the number of revolutions (n) required to cover 1100 cm, we use the formula:

\[ n = \frac{\text{Total Distance}}{\text{Circumference}} \]

Substituting the values:

\[ n = \frac{1100 \text{ cm}}{220 \text{ cm}} = 5 \]

### Final Answer
The number of revolutions required to travel a distance of 11 meters is **5**.

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