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

345 m
345 m

44 m
44 m

10 m
10 m

220 m

Answer 1

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

1. **Original radius of circle O:** 14 meters
2. **Scale factor:** 2.5

Now, we calculate the new radius of circle O' (R'):

\[
R' = \text{Original Radius} \times \text{Scale Factor} = 14 \, \text{m} \times 2.5 = 35 \, \text{m}
\]

Next, we can calculate the circumference of circle O' using the formula for the circumference of a circle:

\[
C = 2 \pi R
\]

Substituting R' into the formula:

\[
C' = 2 \pi (35 \, \text{m}) = 70 \pi \, \text{m}
\]

Using \(\pi \approx 3.14\) to find the numerical value of \(C'\):

\[
C' \approx 70 \times 3.14 = 219.8 \, \text{m} \approx 220 \, \text{m}
\]

Therefore, the circumference of circle O' is approximately **220 m**.

So the correct answer is:
**220 m**.