Diameter of a car wheel is 21cm. A car driver moving at the speed of 66km/hr takes 36 seconds to reach a destination. How many revolutions will the wheel make during the journey?

Options

A. 1800
B. 1500
C. 1200
D. 1000

Answer

To find the number of revolutions the wheel makes during the journey, we can follow these steps:

### Step 1: Calculate the distance traveled by the car.
We know that distance = speed × time.

- Speed = 66 km/hr
- Time = 36 seconds

First, we need to convert the speed from km/hr to m/s:
\[ \text{Speed in m/s} = \frac{66 \text{ km/hr} \times 1000 \text{ m/km}}{3600 \text{ s/hr}} = \frac{66000}{3600} = 18.33 \text{ m/s} \]

Now, we calculate the distance traveled in 36 seconds:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 18.33 \text{ m/s} \times 36 \text{ s} = 660 \text{ m} \]

### Step 2: Calculate the circumference of the wheel.
The circumference \( C \) of a circle is given by the formula:
\[ C = \pi \times d \]
where \( d \) is the diameter.

Given that the diameter of the wheel is 21 cm, we convert it to meters:
\[ d = 21 \text{ cm} = 0.21 \text{ m} \]

Now, we can calculate the circumference:
\[ C = \pi \times 0.21 \approx 3.14 \times 0.21 \approx 0.660 \text{ m} \]

### Step 3: Calculate the number of revolutions.
The number of revolutions \( N \) made by the wheel is given by:
\[ N = \frac{\text{Distance}}{\text{Circumference}} \]

Substituting the values we calculated:
\[ N = \frac{660 \text{ m}}{0.660 \text{ m}} = 1000 \]

### Final Answer:
The wheel will make **1000 revolutions** during the journey.

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