The diameter of a wheel is 84 cm. How many revolution will it make to cover 792 m ?

Answer

To solve the problem of how many revolutions a wheel with a diameter of 84 cm will make to cover a distance of 792 m, we can follow these steps:

### Step 1: Convert the diameter to radius
The diameter of the wheel is given as 84 cm. The radius (r) can be calculated using the formula:
\[ r = \frac{\text{Diameter}}{2} \]
So,
\[ r = \frac{84 \, \text{cm}}{2} = 42 \, \text{cm} \]

**Hint:** Remember that the radius is half of the diameter.

### Step 2: Calculate the circumference of the wheel
The circumference (C) of a circle is calculated using the formula:
\[ C = 2 \pi r \]
Using \( \pi \approx \frac{22}{7} \):
\[ C = 2 \times \frac{22}{7} \times 42 \]
\[ C = \frac{44}{7} \times 42 \]
\[ C = \frac{1848}{7} \]
\[ C = 264 \, \text{cm} \]

**Hint:** The circumference is the distance the wheel covers in one complete revolution.

### Step 3: Convert the distance to centimeters
The distance to be covered is given as 792 m. We need to convert this distance into centimeters:
\[ 792 \, \text{m} = 792 \times 100 \, \text{cm} = 79200 \, \text{cm} \]

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

### Step 4: Calculate the number of revolutions
To find the number of revolutions (N), we divide the total distance covered by the circumference of the wheel:
\[ N = \frac{\text{Total Distance}}{\text{Circumference}} \]
\[ N = \frac{79200 \, \text{cm}}{264 \, \text{cm}} \]
\[ N = 300 \]

**Hint:** The number of revolutions tells you how many times the wheel has turned to cover the total distance.

### Final Answer
The wheel will make **300 revolutions** to cover 792 m.

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