Question

page 7 of 7 Similar Circles Quick Check 5 of 55 of 5 Items 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 220 m Skip to navigation

Answer 1

To find the circumference of circle O′ after dilation, we first need to calculate the circumference of the original circle O.

The formula for the circumference \(C\) of a circle is given by:

\[
C = 2\pi r
\]

where \(r\) is the radius of the circle.

Given that the radius of circle O is 14 meters:

\[
C = 2\pi \times 14 = 28\pi \text{ meters}
\]

Next, since the circle is dilated by a scale factor of 2.5, we can find the new radius \(r'\) of circle O′:

\[
r' = 2.5 \times 14 = 35 \text{ meters}
\]

Now we can calculate the circumference of circle O′ using the new radius:

\[
C' = 2\pi r' = 2\pi \times 35 = 70\pi \text{ meters}
\]

Now we can approximate \(70\pi\) using \( \pi \approx 3.14\):

\[
70\pi \approx 70 \times 3.14 = 219.8 \text{ meters}
\]

Since the option closest to 220 m is listed among your choices, the answer is:

**220 m**.