The diameter of a cycle wheel is 14cm. A cyclist takes 30 minutes to reach a destination at a speed of 11km/hr.How many revolutions will the wheel make during the journey?

Options

A. 12500
B. 15000
C. 17750
D. 20000

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Calculate the Circumference of the Wheel
The circumference of a circle (which is the distance covered in one complete revolution) can be calculated using the formula:
\[ \text{Circumference} = \pi \times D \]
where \(D\) is the diameter of the wheel.

Given:
- Diameter \(D = 14 \text{ cm}\)

Using \(\pi \approx \frac{22}{7}\):
\[ \text{Circumference} = \frac{22}{7} \times 14 = 44 \text{ cm} \]

### Step 2: Convert the Circumference to Meters
Since the speed is given in kilometers per hour, we need to convert the circumference from centimeters to meters:
\[ 44 \text{ cm} = \frac{44}{100} \text{ m} = 0.44 \text{ m} \]

### Step 3: Calculate the Total Distance Covered
Next, we need to calculate the total distance covered by the cyclist during the journey. We use the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Given:
- Speed = 11 km/hr
- Time = 30 minutes = \(\frac{30}{60} = 0.5\) hours

Now, substituting the values:
\[ \text{Distance} = 11 \text{ km/hr} \times 0.5 \text{ hr} = 5.5 \text{ km} \]

Convert kilometers to meters:
\[ 5.5 \text{ km} = 5.5 \times 1000 \text{ m} = 5500 \text{ m} \]

### Step 4: Calculate the Number of Revolutions
Now, we can find the number of revolutions made by the wheel using the formula:
\[ \text{Number of Revolutions} = \frac{\text{Total Distance}}{\text{Circumference}} \]

Substituting the values:
\[ \text{Number of Revolutions} = \frac{5500 \text{ m}}{0.44 \text{ m}} = 12500 \]

### Conclusion
The wheel will make **12,500 revolutions** during the journey.

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