If the radius of circle O

Question

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.