California Assessment of Student Performance and Progress (CAASPP) Math Practice Exam

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What is the formula for the area of a circle?

A = 2πr
A = πr²
A = πd
A = 4πr²

The correct answer is: A = πr²

The formula for the area of a circle is derived from the geometry of the circle, where "A" represents the area, "π" (pi) is a constant approximately equal to 3.14159, and "r" stands for the radius of the circle. The area of a circle is calculated as the space contained within its boundaries, and this is represented mathematically by the formula A = πr². Here, squaring the radius (r²) communicates that the area increases with the square of the radius, highlighting the significant impact of the radius on the overall area as it grows. In other contexts, alternatives to this formula present different measurements or geometrical properties. For instance, using the diameter (d), the circumference formula conveys length rather than area, which is vital for linear measurements but insufficient for calculating the space within a circle. Additionally, some options reflect dimensions or properties not directly related to area. Therefore, the given choice perfectly encapsulates the relationship between a circle's radius and its area.