The circumference of a circle formula is:
C=2πr, where C=circumference and r=radius
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C=πd, where C=circumference and d=diameter.
*This is a simplified formula from the first since 2r=d.*
Either way, we must find the diameter (or 2r) first to calculate the circumference.
We know that the two circles share the same center point since all circles are similar, meaning their radii differ, but the point remains in the same location. Therefore, the 9ft. diameter in the purple circle is part of the diameter in the yellow circle. Remember, it doesn’t matter wether the diameter is shown horizontally across the circle or vertically across the circle; the diameter doesn’t change because every point on the circle to the center is equidistant. So, picture rotating the diameter 90° clockwise so that it is vertical to the purple circle. Now the 2.5ft is joined with the 9ft. diameter in the purple circle. Because the yellow circle has the same thickness all around, we can assume that the part right above the rotated diameter in the purple circle is also 2.5ft. So, the yellow circle has a total diameter of:
d=2.5+9+2.5
d=2(2.5)+9
d=5+9
d=14ft.
So, let’s plug d=14ft into the circumference formula to find the circumference of the yellow circle:
C=π(14)
C≈43.982
Rounded to the nearest hundredth, the yellow circle has a circumference of 43.98
Answer: yellow circle circumference is 43.98ft.
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The purple circle has a diameter of 9ft. So, d=9 in the circumference formula.
C=π(9)
C≈28.274
Rounded to the meta test hundredth: 28.27 is the circumference of the purple circle.
Answer: the purple circle has a circumference of 28.27ft.
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Answers:
Yellow circle: 43.98ft.
Purple circle: 28.27ft.