A road roller has wheels of radius 70 cm. It has to work on an 88 km road. How many revolutions of the wheel will be required for the road roller to cover the entire length of the road once? Take `pi = (22)/(7).`

Answer

To solve the problem step by step, we will calculate the number of revolutions required for a road roller with wheels of radius 70 cm to cover an 88 km road.

### Step 1: Find the circumference of the wheel.
The formula for the circumference \( C \) of a circle is given by:
\[ C = 2 \pi r \]
where \( r \) is the radius of the wheel.

Given:
- Radius \( r = 70 \) cm
- \( \pi = \frac{22}{7} \)

Substituting the values into the formula:
\[ C = 2 \times \frac{22}{7} \times 70 \]

### Step 2: Calculate the circumference.
Calculating the above expression:
\[ C = 2 \times \frac{22 \times 70}{7} \]
\[ C = 2 \times 22 \times 10 = 440 \text{ cm} \]

### Step 3: Convert the circumference from centimeters to kilometers.
Since the total distance of the road is given in kilometers, we need to convert the circumference from centimeters to kilometers.

We know:
- \( 1 \text{ km} = 100,000 \text{ cm} \)

So,
\[ 440 \text{ cm} = \frac{440}{100,000} \text{ km} = 0.0044 \text{ km} \]

### Step 4: Calculate the number of revolutions required to cover 88 km.
To find the number of revolutions \( N \) needed to cover 88 km, we can use the formula:
\[ N = \frac{\text{Total Distance}}{\text{Circumference}} \]

Substituting the values:
\[ N = \frac{88 \text{ km}}{0.0044 \text{ km}} \]

### Step 5: Perform the division.
Calculating the above expression:
\[ N = 88 \div 0.0044 \]

To make the calculation easier, we can multiply both the numerator and the denominator by 10,000 (to eliminate the decimal):
\[ N = \frac{88 \times 10,000}{0.0044 \times 10,000} = \frac{880,000}{44} \]

Now, performing the division:
\[ N = 20,000 \]

### Final Answer:
The number of revolutions required for the road roller to cover the entire length of the 88 km road is **20,000 revolutions**.

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