Here are the essential concepts you must grasp in order to answer the question correctly.
Direct Variation
Direct variation describes a relationship between two variables where one variable is a constant multiple of the other. In this case, the circumference (C) of a circle varies directly with its radius (r), meaning C = k * r, where k is a constant. This concept is essential for understanding how changes in the radius affect the circumference.
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Circumference of a Circle
The circumference of a circle is the distance around it and can be calculated using the formula C = 2πr, where r is the radius. This formula highlights the relationship between the radius and the circumference, reinforcing the concept of direct variation. Knowing this formula allows for the calculation of circumference when the radius is known.
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Proportional Relationships
Proportional relationships occur when two quantities maintain a constant ratio. In the context of this problem, as the radius increases, the circumference increases proportionally. Understanding this relationship is crucial for solving the problem, as it allows for the use of ratios to find the new circumference based on the change in radius.
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