Hannah constructed two similar circles as seen in the image below. If the arc length of the larger circle is , which of the following would be true?
A. The arc length of the smaller circle is proportional to the radius of the smaller circle.
B. The arc length of the larger circle is double the arc length of the larger circle.
C. The arc length of the larger circle is equal to half the arc length of the smaller circle.
D. The arc length of the smaller circle is proportional to the central angle of the arc of the larger circle.
i like butthole
i have the sam problem, but the larger circle was 4Π
its the a.
To determine the correct answer, let's first understand the relationship between the arc length of a circle and its radius.
The formula for the arc length of a circle is given by:
Arc Length = (Central Angle / 360°) * (2 * π * Radius)
So, the arc length of a circle is directly proportional to both the central angle (in degrees) and the radius of the circle.
Now let's consider the two similar circles constructed by Hannah. Since the circles are similar, their corresponding parts will be proportional.
According to option A, the arc length of the smaller circle is proportional to the radius of the smaller circle. This statement is incorrect because the relationship between the arc length and the radius is direct proportionality, not the other way around. Therefore, option A is not true.
According to option B, the arc length of the larger circle is double the arc length of the larger circle. This statement seems to have a typo, as it states that the arc length of the larger circle is double itself. We can assume this is meant to say "double the arc length of the smaller circle." However, without the corrected statement, option B cannot be considered true.
According to option C, the arc length of the larger circle is equal to half the arc length of the smaller circle. This statement is incorrect because, as explained earlier, the arc length is directly proportional to the radius of the circle. Since the circles are similar and their parts are proportional, the arc length of the larger circle will be greater than the arc length of the smaller circle. Therefore, option C is not true.
According to option D, the arc length of the smaller circle is proportional to the central angle of the arc of the larger circle. This statement is accurate as both the arc length and the central angle are directly proportional to the radius of the circle. Since the circles are similar, the corresponding parts are proportional, and hence the statement in option D is true.
Therefore, the correct answer is option D: The arc length of the smaller circle is proportional to the central angle of the arc of the larger circle.
eat 12 apple at any given time
The answer is heil hitler.
too many typos to proceed.
No diagram, but then none needed, since all circles are similar.