The wheel of a lorry has radius 182 cm What are the no of revolutions lorry will make in a minute if its speed is 66Km/hr?

To solve this problem, we'll need to follow these steps:

### Step 1: Convert the speed of the lorry from km/hr to cm/min
Given:
- Speed of the lorry = 66 km/hr

First, convert the speed to cm/min:
- \( 1 \, \text{km} = 1000 \, \text{m} = 100000 \, \text{cm} \)
- \( 1 \, \text{hr} = 60 \, \text{min} \)

So, the speed in cm/min is:
\[
66 \, \text{km/hr} = 66 \times 100000 \, \text{cm/hr} = 6600000 \, \text{cm/hr}
\]
\[
6600000 \, \text{cm/hr} \div 60 \, \text{min/hr} = 110000 \, \text{cm/min}
\]

### Step 2: Calculate the circumference of the wheel
The circumference \( C \) of the wheel is given by the formula:
\[
C = 2\pi r
\]
where \( r \) is the radius of the wheel.

Given:
- Radius of the wheel \( r = 182 \, \text{cm} \)

So, the circumference is:
\[
C = 2 \times \pi \times 182 \, \text{cm} = 364\pi \, \text{cm}
\]

### Step 3: Calculate the number of revolutions per minute
The number of revolutions \( N \) made by the wheel in one minute can be found by dividing the distance traveled in one minute by the circumference of the wheel:
\[
N = \frac{\text{Distance traveled in one minute}}{\text{Circumference of the wheel}}
\]
\[
N = \frac{110000 \, \text{cm}}{364\pi \, \text{cm}} \approx \frac{110000}{1143.86} \approx 96.15
\]

### Final Answer:
The lorry will make approximately **96** revolutions per minute.

### Would you like a more detailed explanation or have any other questions?

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Here are 8 related questions to expand your understanding:
1. How would the number of revolutions change if the lorry's speed increased to 80 km/hr?
2. What would be the number of revolutions if the radius of the wheel were halved?
3. How does the number of revolutions change if the lorry's speed is reduced to 33 km/hr?
4. What is the relation between the radius of the wheel and the number of revolutions?
5. If the wheel's circumference were doubled, how would that affect the number of revolutions?
6. What is the distance covered by the lorry in 10 minutes?
7. How would the result change if the radius of the wheel was given in meters instead of centimeters?
8. What is the time required for the lorry to travel 1 km at the given speed?

**Tip:** When working with circular motion problems, always ensure units are consistent, especially when dealing with speed and distances.

Learn how to calculate the number of revolutions a lorry wheel makes in a minute at a speed of 66 km/hr. Understand the relationship between speed, wheel radius, and circular motion concepts. Suitable for high school students studying geometry and trigonometry.

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