The diameter of the driving wheel of a cart is 154 cm. Calculate the revolutions per minute [RPM] of the wheel in order to keep a speed of 33 kilo metre per hour.

Options

A. 114
B. 112
C. 110
D. 108

Answer

To solve the problem of calculating the revolutions per minute (RPM) of the wheel of a cart with a diameter of 154 cm, in order to maintain a speed of 33 kilometers per hour, we can follow these steps:

### Step 1: Convert Speed from km/h to m/min
First, we need to convert the speed from kilometers per hour to meters per minute.

\[ \text{Speed} = 33 \text{ km/h} = 33 \times 1000 \text{ m/h} = 33000 \text{ m/h} \]

Since there are 60 minutes in an hour, we convert this to meters per minute:

\[ \text{Speed in m/min} = \frac{33000 \text{ m/h}}{60} = 550 \text{ m/min} \]

### Step 2: Convert Diameter to Radius in Meters
Next, we convert the diameter of the wheel from centimeters to meters.

\[ \text{Diameter} = 154 \text{ cm} = \frac{154}{100} \text{ m} = 1.54 \text{ m} \]

Now, we find the radius:

\[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{1.54}{2} = 0.77 \text{ m} \]

### Step 3: Calculate the Circumference of the Wheel
The circumference (C) of the wheel can be calculated using the formula:

\[ C = 2 \pi R \]

Using \( \pi \approx \frac{22}{7} \):

\[ C = 2 \times \frac{22}{7} \times 0.77 \approx 4.84 \text{ m} \]

### Step 4: Calculate the Number of Revolutions per Minute
To find the number of revolutions per minute, we divide the distance traveled in one minute by the circumference of the wheel.

\[ \text{Revolutions per minute (RPM)} = \frac{\text{Distance in m/min}}{\text{Circumference in m}} = \frac{550}{4.84} \]

Calculating this gives:

\[ \text{RPM} \approx 113.66 \]

### Step 5: Round the Result
Since RPM is typically rounded to the nearest whole number, we round 113.66 to 114.

Thus, the final answer is:

\[ \text{RPM} \approx 114 \]

### Summary
The revolutions per minute (RPM) of the wheel to maintain a speed of 33 km/h is approximately 114.

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