Which of the following is involved in an informal argument for the formula for the circumference of a circle?
A. Diameter
B. Perimeter
C. Chord
D. Area
Answer (2)
The circumference of a circle is directly related to its diameter by the formula C = π d .
The perimeter of a circle is the same as its circumference.
Chords and area are not directly involved in the circumference formula.
Therefore, the perimeter is the most direct answer. P er im e t er
Explanation
Analyze the options The question asks us to identify which term is directly related to the circumference of a circle. Let's consider the options:
Diameter: The diameter is the distance across the circle through the center. The circumference C is calculated using the formula C = π d , where d is the diameter.
Perimeter: The perimeter of a circle is the same as its circumference.
Chord: A chord is a line segment connecting two points on the circle. While chords are related to circles, they are not directly used in the basic circumference formula.
Area: The area of a circle is calculated using the formula A = π r 2 , where r is the radius. Area is not directly involved in the circumference formula.
Recall the circumference formula The formula for the circumference of a circle is:
C = π d
Where:
C is the circumference
π (pi) is a mathematical constant approximately equal to 3.14159
d is the diameter of the circle
Since the circumference is the perimeter of the circle, the perimeter is also directly related to the circumference.
Determine the most direct answer Both the diameter and the perimeter are closely related to the circumference. However, the perimeter is the circumference. Therefore, perimeter is the most direct answer.
Examples
Understanding the circumference of a circle is crucial in many real-world applications. For example, when designing a circular running track, knowing the circumference helps determine the distance runners will cover in one lap. Similarly, in manufacturing, calculating the circumference of cylindrical objects is essential for determining the amount of material needed to wrap around them. Even in everyday life, estimating the circumference of a circular object can help you determine if it will fit in a particular space or if you have enough ribbon to wrap around a gift.
The term most involved in an informal argument for the formula for the circumference of a circle is 'perimeter,' as it is defined as the distance around the circle, also known as the circumference. While diameter is important for the calculation, the perimeter directly corresponds to the circumference itself. Thus, the chosen option is 'Perimeter.'
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