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If the radius of circle O is 14 meters and it is dilated by a scale factor of 2.5, then what will be the circumference of circle O′ ?(1 point)

Responses

220 m
220 m

10 m
10 m

345 m
345 m

44 m
44 m

1 answer

To find the circumference of circle \( O' \) after dilation, we first need to determine the new radius after applying the scale factor.

  1. Find the new radius: The original radius of circle \( O \) is 14 meters. When it is dilated by a scale factor of 2.5, the new radius \( r' \) is calculated as:

    \[ r' = \text{scale factor} \times \text{original radius} = 2.5 \times 14 = 35 \text{ meters} \]

  2. Calculate the circumference: The formula for the circumference \( C \) of a circle is given by:

    \[ C = 2\pi r \]

    Substituting the new radius \( r' \):

    \[ C' = 2\pi \times 35 \] \[ C' = 70\pi \]

    To get the numerical value, we can approximate \( \pi \) as 3.14:

    \[ C' \approx 70 \times 3.14 = 219.8 \text{ meters} \]

  3. Choose the closest answer: The closest option from the responses given is:

    220 m