To find the circumference of circle 0' after the dilation, we first need to determine the new radius of circle 0' after applying the scale factor.
- Original radius of circle 0: 14 meters
- Scale factor: 2.5
New radius of circle 0' can be calculated as: \[ \text{New radius} = \text{Original radius} \times \text{Scale factor} = 14 \times 2.5 = 35 \text{ meters} \]
Next, we use the formula for the circumference \( C \) of a circle, which is given by: \[ C = 2 \pi r \] where \( r \) is the radius.
Now substituting the new radius: \[ C = 2 \pi (35) = 70 \pi \]
We need to calculate the numerical value of \( 70 \pi \). Using \( \pi \approx 3.14 \): \[ C \approx 70 \times 3.14 = 219.8 \]
Rounding this to the nearest whole number gives us approximately 220.
Thus, the circumference of circle 0' is: \[ \boxed{220} \]