To find the circumference of circle O′ after dilation, we first need to calculate the original circumference of circle O. The formula for the circumference (C) of a circle is:
\[ C = 2\pi r \]
Where \( r \) is the radius of the circle.
- The original radius of circle O is 14 meters.
- Calculate the original circumference:
\[ C_O = 2\pi \times 14 = 28\pi , \text{meters} \]
Now, since the circle is dilated by a scale factor of 2.5, we can find the new radius (r′) of circle O′:
- The new radius is:
\[ r′ = 2.5 \times 14 = 35 , \text{meters} \]
- Now we calculate the circumference of circle O′:
\[ C_{O′} = 2\pi r′ = 2\pi \times 35 = 70\pi , \text{meters} \]
- To approximate, we can use \( \pi \approx 3.14 \):
\[ C_{O′} \approx 70 \times 3.14 = 219.8 , \text{meters} \]
Rounding to the nearest whole number gives us approximately 220 meters.
Thus, the circumference of circle O′ is 220 m.