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
44 m
44 m
345 m
345 m
10 m
10 m
220 m
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
44 m
44 m
345 m
345 m
10 m
10 m
220 m
Answers
Answered by
GPT-4o mini
To find the circumference of circle O′ after dilation, we first need to calculate the original circumference of circle O. The formula for the circumference (C) of a circle is:
\[ C = 2\pi r \]
Where \( r \) is the radius of the circle.
1. The original radius of circle O is 14 meters.
2. Calculate the original circumference:
\[ C_O = 2\pi \times 14 = 28\pi \, \text{meters} \]
Now, since the circle is dilated by a scale factor of 2.5, we can find the new radius (r′) of circle O′:
3. The new radius is:
\[ r′ = 2.5 \times 14 = 35 \, \text{meters} \]
4. Now we calculate the circumference of circle O′:
\[ C_{O′} = 2\pi r′ = 2\pi \times 35 = 70\pi \, \text{meters} \]
5. To approximate, we can use \( \pi \approx 3.14 \):
\[ C_{O′} \approx 70 \times 3.14 = 219.8 \, \text{meters} \]
Rounding to the nearest whole number gives us approximately 220 meters.
Thus, the circumference of circle O′ is **220 m**.
\[ C = 2\pi r \]
Where \( r \) is the radius of the circle.
1. The original radius of circle O is 14 meters.
2. Calculate the original circumference:
\[ C_O = 2\pi \times 14 = 28\pi \, \text{meters} \]
Now, since the circle is dilated by a scale factor of 2.5, we can find the new radius (r′) of circle O′:
3. The new radius is:
\[ r′ = 2.5 \times 14 = 35 \, \text{meters} \]
4. Now we calculate the circumference of circle O′:
\[ C_{O′} = 2\pi r′ = 2\pi \times 35 = 70\pi \, \text{meters} \]
5. To approximate, we can use \( \pi \approx 3.14 \):
\[ C_{O′} \approx 70 \times 3.14 = 219.8 \, \text{meters} \]
Rounding to the nearest whole number gives us approximately 220 meters.
Thus, the circumference of circle O′ is **220 m**.