The radius of a wheel of a cycle is 70 cm and it takes 5 minutes to make 3000 rotations . Find the speed of the cycle in km per hour . (Take `pi=(22)/(7))`.

Answer

To find the speed of the cycle in kilometers per hour, we will follow these steps:

### Step 1: Calculate the perimeter of the wheel
The perimeter (circumference) of a circle is given by the formula:
\[ \text{Perimeter} = 2 \pi r \]
Where \( r \) is the radius. Given that the radius \( r = 70 \) cm and \( \pi = \frac{22}{7} \), we can substitute these values into the formula.

\[ \text{Perimeter} = 2 \times \frac{22}{7} \times 70 \]

### Step 2: Simplify the calculation
Calculating the above expression:
\[ \text{Perimeter} = 2 \times \frac{22 \times 70}{7} = 2 \times 220 = 440 \text{ cm} \]

### Step 3: Calculate the total distance covered in 3000 rotations
The distance covered in one rotation is equal to the perimeter of the wheel. Therefore, the distance covered in 3000 rotations is:
\[ \text{Distance} = 440 \text{ cm} \times 3000 = 132000 \text{ cm} \]

### Step 4: Convert the distance from centimeters to kilometers
To convert centimeters to kilometers, we use the conversion factor \( 1 \text{ km} = 100000 \text{ cm} \):
\[ \text{Distance in km} = \frac{132000 \text{ cm}}{100000} = 1.32 \text{ km} \]

### Step 5: Convert the time from minutes to hours
The time taken is given as 5 minutes. To convert this into hours:
\[ \text{Time in hours} = \frac{5}{60} = \frac{1}{12} \text{ hours} \]

### Step 6: Calculate the speed of the cycle
Speed is calculated using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Substituting the values we have:
\[ \text{Speed} = \frac{1.32 \text{ km}}{\frac{1}{12} \text{ hours}} = 1.32 \times 12 = 15.84 \text{ km/h} \]

### Final Answer
The speed of the cycle is:
\[ \text{Speed} = 15.84 \text{ km/h} \]

---