To find the circumference of circle O' after dilation, we first need to calculate the circumference of the original circle O and then apply the scale factor.
The formula for the circumference \( C \) of a circle is given by:
\[ C = 2 \pi r \]
where \( r \) is the radius of the circle.
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Calculate the original circumference of circle O:
- The radius \( r \) is 14 meters. \[ C = 2 \pi (14) = 28\pi , \text{meters} \]
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Determine the new radius after dilation:
- The scale factor for dilation is 2.5. \[ r' = 2.5 \times 14 = 35 , \text{meters} \]
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Calculate the circumference of the dilated circle O′: \[ C' = 2 \pi (35) = 70\pi , \text{meters} \]
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Approximate \( \pi \) as 3.14 for numerical calculation: \[ C' \approx 70 \times 3.14 = 219.8 , \text{meters} \]
If we round it off for the answer choices given, we see that the closest response to 219.8 m is:
220 m
1 answer