A circular wheel if radius 28 cm makes 300 revolutions per minute. Find the speed of the wheel in kilometre per hour.

Answer

To find the speed of a circular wheel with a radius of 28 cm that makes 300 revolutions per minute, we can follow these steps:

### Step 1: Calculate the Circumference of the Wheel
The circumference \( C \) of a circle is given by the formula:
\[ C = 2 \pi r \]
Where \( r \) is the radius. Given that the radius \( r = 28 \) cm, we can substitute this value into the formula:
\[ C = 2 \times \frac{22}{7} \times 28 \]
Calculating this gives:
\[ C = 2 \times \frac{22}{7} \times 28 = 2 \times 22 \times 4 = 176 \text{ cm} \]

### Step 2: Calculate the Number of Revolutions per Second
We know that the wheel makes 300 revolutions per minute. To find the number of revolutions per second, we divide by 60:
\[ \text{Revolutions per second} = \frac{300}{60} = 5 \text{ revolutions/second} \]

### Step 3: Calculate the Distance Covered in One Second
The distance covered in one second can be calculated by multiplying the number of revolutions per second by the circumference:
\[ \text{Distance in 1 second} = \text{Revolutions per second} \times C = 5 \times 176 = 880 \text{ cm} \]

### Step 4: Convert Distance from cm to m
To convert the distance from centimeters to meters, we divide by 100:
\[ 880 \text{ cm} = \frac{880}{100} = 8.8 \text{ m} \]

### Step 5: Calculate Speed in Meters per Minute
Since we have the distance covered in 1 second, we need to convert this to a minute:
\[ \text{Distance in 1 minute} = 880 \text{ cm} \times 60 = 52800 \text{ cm} = 528 \text{ m} \]
Thus, the speed in meters per minute is:
\[ \text{Speed} = 8.8 \text{ m/s} \times 60 = 528 \text{ m/min} \]

### Step 6: Convert Speed to Kilometers per Hour
To convert speed from meters per minute to kilometers per hour, we use the conversion factor \( \frac{18}{5} \):
\[ \text{Speed in km/h} = 8.8 \times \frac{18}{5} = \frac{158.4}{5} = 31.68 \text{ km/h} \]

### Conclusion
Therefore, the speed of the wheel is:
\[ \text{Speed} = 31.68 \text{ km/h} \]

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