The wheel of an engine 300 cm in circumfrence makes 10 revolutions in 6 seconds What is the speed of the wheel (in km/h)?

Options

A. 18
B. 20
C. 27
D. 36

Answer

To find the speed of the wheel in km/h, we will follow these steps:

### Step 1: Calculate the total distance traveled in 10 revolutions.
The circumference of the wheel is given as 300 cm. Therefore, the distance traveled in one revolution is 300 cm.

For 10 revolutions:
\[ \text{Total Distance} = \text{Circumference} \times \text{Number of Revolutions} = 300 \, \text{cm} \times 10 = 3000 \, \text{cm} \]

### Step 2: Calculate the time taken for 10 revolutions.
The time taken for 10 revolutions is given as 6 seconds.

### Step 3: Calculate the speed in cm/s.
Speed is calculated as distance divided by time. Thus, we can calculate the speed in cm/s:
\[ \text{Speed} = \frac{\text{Total Distance}}{\text{Time}} = \frac{3000 \, \text{cm}}{6 \, \text{s}} = 500 \, \text{cm/s} \]

### Step 4: Convert the speed from cm/s to m/s.
To convert cm/s to m/s, we divide by 100 (since 1 m = 100 cm):
\[ \text{Speed in m/s} = \frac{500 \, \text{cm/s}}{100} = 5 \, \text{m/s} \]

### Step 5: Convert the speed from m/s to km/h.
To convert m/s to km/h, we multiply by 18/5 (or simply multiply by 3.6):
\[ \text{Speed in km/h} = 5 \, \text{m/s} \times \frac{18}{5} = 18 \, \text{km/h} \]

### Final Answer:
The speed of the wheel is **18 km/h**.

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