The diameter of a wheel is 98 cm. The number of revolutions in which it will have to cover a distance of 1540 m is

Options

A. 500
B. 600
C. 700
D. 800

Answer

To solve the problem step by step, we need to find the number of revolutions a wheel with a diameter of 98 cm will make to cover a distance of 1540 m.

### 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 \( d = 98 \) cm

Using \( \pi \approx \frac{22}{7} \):
\[ C = \frac{22}{7} \times 98 \]

### Step 2: Simplify the calculation.
First, simplify the multiplication:
\[ C = \frac{22 \times 98}{7} \]

Now, divide 98 by 7:
\[ 98 \div 7 = 14 \]

So, we have:
\[ C = 22 \times 14 \]
\[ C = 308 \text{ cm} \]

### Step 3: Convert the total distance from meters to centimeters.
The total distance to be covered is given as 1540 m. We need to convert this distance into centimeters:
\[ 1 \text{ m} = 100 \text{ cm} \]
Thus,
\[ 1540 \text{ m} = 1540 \times 100 \text{ cm} = 154000 \text{ cm} \]

### Step 4: Calculate the number of revolutions.
The number of revolutions (N) can be calculated using the formula:
\[ N = \frac{\text{Total Distance}}{\text{Circumference}} \]
Substituting the values we have:
\[ N = \frac{154000 \text{ cm}}{308 \text{ cm}} \]

### Step 5: Perform the division.
Now, we divide:
\[ N = \frac{154000}{308} \]

Calculating this gives:
\[ N = 500 \]

### Final Answer:
The number of revolutions the wheel will make to cover a distance of 1540 m is **500**.

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