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

220 m
220 m

10 m
10 m

44 m
44 m

345 m

Answer 1

To find the circumference of circle \( O' \) after dilation, we first calculate the radius of the new circle \( O' \).

1. The original radius of circle \( O \) is 14 meters.
2. The scale factor for dilation is 2.5.

Now, calculate the new radius:

\[
\text{New radius} = 14 \, \text{m} \times 2.5 = 35 \, \text{m}
\]

Next, we calculate the circumference of circle \( O' \) using the formula for the circumference of a circle, which is:

\[
C = 2\pi r
\]

Substituting the new radius into the formula:

\[
C = 2\pi(35) = 70\pi
\]

Now, we can approximate \( \pi \) as 3.14 for calculation:

\[
C \approx 70 \times 3.14 = 219.8 \, \text{m}
\]

Rounding gives us approximately 220 meters.

Therefore, the circumference of circle \( O' \) is **220 m**.