What formula is used to find the area of a circle?

Study for the Massachusetts 3rd Class Engineer Exam. Access flashcards and multiple choice questions with hints and explanations. Prepare for success on your exam!

The area of a circle is calculated using the formula A = πr², where A represents the area and r represents the radius of the circle. This formula derives from the relationship between the circle’s radius and its area.

To understand why this is the case, it’s helpful to visualize a circle as being made up of many tiny triangles pointing towards the center. The radius extends from the center of the circle to its edge, and by calculating the area of these triangles and summing them up, one can derive the formula for the area of the entire circle.

The π (pi) in the formula is a constant that represents the ratio of the circumference of any circle to its diameter, which approximately equals 3.14159. The square of the radius indicates that the area increases with the square of the radius — meaning that if the radius doubles, the area becomes four times larger (since 2² = 4).

Using this understanding, it becomes clear that the other formulas provided do not accurately represent the area of a circle. For instance, A = πd uses the diameter rather than the radius, while A = 2πr calculates the circumference of the circle rather than its area. The formula A = r²

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