Find the diameter of a wheel that makes 113 revolutions to go 2 km 26 decametres ? `(pi = 22/7)`

Answer

To find the diameter of a wheel that makes 113 revolutions to cover a distance of 2 km 26 decametres, we can follow these steps:

### Step 1: Convert the total distance into meters
We know that:
- 1 kilometer = 1000 meters
- 1 decametre = 10 meters

So, we convert the total distance:
- 2 kilometers = 2 × 1000 = 2000 meters
- 26 decametres = 26 × 10 = 260 meters

Now, we add these two distances together:
\[ \text{Total distance} = 2000 \text{ meters} + 260 \text{ meters} = 2260 \text{ meters} \]

### Step 2: Calculate the distance covered in one revolution
To find the distance covered in one revolution, we divide the total distance by the number of revolutions:
\[ \text{Distance covered in one revolution} = \frac{\text{Total distance}}{\text{Number of revolutions}} = \frac{2260 \text{ meters}}{113} \]

Calculating this gives:
\[ \text{Distance covered in one revolution} = 20 \text{ meters} \]

### Step 3: Relate the distance covered in one revolution to the circumference of the wheel
The distance covered in one revolution is equal to the circumference of the wheel. Therefore:
\[ \text{Circumference of the wheel} = 20 \text{ meters} \]

### Step 4: Use the formula for circumference to find the diameter
The formula for the circumference \( C \) of a circle is given by:
\[ C = \pi d \]
where \( d \) is the diameter.

We can rearrange this formula to find the diameter:
\[ d = \frac{C}{\pi} \]

Substituting the known values:
\[ d = \frac{20 \text{ meters}}{\pi} \]

Given \( \pi = \frac{22}{7} \):
\[ d = \frac{20}{\frac{22}{7}} = 20 \times \frac{7}{22} = \frac{140}{22} \]

### Step 5: Simplify the diameter
Now, we simplify \( \frac{140}{22} \):
\[ d = \frac{70}{11} \text{ meters} \]

### Final Answer
The diameter of the wheel is:
\[ \text{Diameter} = \frac{70}{11} \text{ meters} \]

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