Question

if the radius of the 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?

Answer 1

To find the circumference of circle O before the dilation, we can use the formula for the circumference of a circle:

\[
C = 2 \pi r
\]

where \( C \) is the circumference and \( r \) is the radius.

Given that the radius \( r \) is 14 meters, we can substitute this value into the formula:

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

Now to calculate the circumference after the circle is dilated by a scale factor of 2.5. The new radius after dilation can be calculated as follows:

\[
\text{New Radius} = \text{Original Radius} \times \text{Scale Factor} = 14 \times 2.5 = 35 \text{ meters}
\]

Now, we can find the new circumference using the new radius:

\[
C_{\text{new}} = 2 \pi (35) = 70 \pi \text{ meters}
\]

Thus, the circumference of circle O after dilation is \( 70 \pi \) meters, which is approximately:

\[
70 \pi \approx 70 \times 3.14 \approx 214 \text{ meters}
\]

So the final answer is:

**The circumference of circle O after dilation is \( 70 \pi \) meters or approximately 214 meters.**