The diameter of each wheel of a car is 70 cm. If each wheel rotates 400 times per minute, then the speed of the car (in km/hr) is (Take `pi = (22)/(7)`)

Options

A. 0.528
B. 528
C. 52.8
D. 5.28

Answer

To find the speed of the car in km/hr given the diameter of the wheel and the number of rotations per minute, we can follow these steps:

### Step 1: Calculate the Circumference of the Wheel
The formula for the circumference \( C \) of a circle is given by:
\[ C = \pi \times d \]
where \( d \) is the diameter.

Given:
- Diameter \( d = 70 \) cm
- \( \pi = \frac{22}{7} \)

Substituting the values:
\[ C = \frac{22}{7} \times 70 \]
Calculating this:
\[ C = \frac{1540}{7} = 220 \text{ cm} \]

### Step 2: Calculate the Distance Covered in One Minute
The distance covered in one rotation is equal to the circumference of the wheel. If the wheel rotates 400 times in one minute, the distance covered in one minute \( D \) is:
\[ D = \text{Number of rotations} \times \text{Circumference} \]
Substituting the values:
\[ D = 400 \times 220 \]
Calculating this:
\[ D = 88000 \text{ cm} \]

### Step 3: Calculate the Distance Covered in One Hour
To find the distance covered in one hour, we multiply the distance covered in one minute by the number of minutes in an hour (60 minutes):
\[ \text{Distance in one hour} = D \times 60 \]
Substituting the value:
\[ \text{Distance in one hour} = 88000 \times 60 \]
Calculating this:
\[ \text{Distance in one hour} = 5280000 \text{ cm} \]

### Step 4: Convert the Distance from cm to km
To convert centimeters to kilometers, we use the conversion factor \( 1 \text{ km} = 100000 \text{ cm} \):
\[ \text{Distance in km} = \frac{5280000}{100000} \]
Calculating this:
\[ \text{Distance in km} = 52.8 \text{ km} \]

### Step 5: Conclusion - Speed of the Car
The speed of the car is therefore:
\[ \text{Speed} = 52.8 \text{ km/hr} \]

### Final Answer
The speed of the car is **52.8 km/hr**.

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