Questions: 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'? 44 m 220 m 345 m 10 m

Solution Steps

To find the circumference of the dilated circle \( O' \), first calculate the new radius by multiplying the original radius by the scale factor. Then, use the formula for the circumference of a circle, \( C = 2\pi r \), where \( r \) is the new radius.

The original radius of circle \( O \) is given as \( r = 14 \) meters. After dilation by a scale factor of \( k = 2.5 \), the new radius \( r' \) is calculated as follows: \[ r' = k \cdot r = 2.5 \cdot 14 = 35 \text{ meters} \]

The circumference \( C' \) of the dilated circle \( O' \) can be found using the formula for the circumference of a circle: \[ C' = 2\pi r' = 2\pi \cdot 35 \] Calculating this gives: \[ C' \approx 219.9115 \text{ meters} \]

Final Answer