Question

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

44 m
44 m

220 m
220 m

10 m
10 m

345 m
345 m

Answer 1

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.

1. **Calculate the original circumference of circle O**:
- The radius \( r \) is 14 meters.
\[
C = 2 \pi (14) = 28\pi \, \text{meters}
\]

2. **Determine the new radius after dilation**:
- The scale factor for dilation is 2.5.
\[
r' = 2.5 \times 14 = 35 \, \text{meters}
\]

3. **Calculate the circumference of the dilated circle O′**:
\[
C' = 2 \pi (35) = 70\pi \, \text{meters}
\]

4. **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**