AFOQT Practice Test

Which formula represents the area of a circle?

1. A = πr²

2. A = 2πr

3. A = r²π

4. A = 1/2πr²

The correct answer is: A = πr²

The formula for the area of a circle is represented by A = πr². This equation derives from the relationship between the radius of the circle and the space contained within its boundaries. In this formula, "A" signifies the area, "π" (pi) is a mathematical constant approximately equal to 3.14159, and "r" is the radius of the circle. The area is calculated by squaring the radius (r²) and then multiplying that value by π. This captures the total surface area within the circular shape. Other formulas presented relate to different geometric properties or formulas relevant to circles but do not calculate the area specifically. For example, the second choice (A = 2πr) is the formula for the circumference of a circle, which is the distance around the circle, not the area. The third choice (A = r²π) is mathematically equivalent to the correct answer but is presented in a less conventional order. The final choice, (A = 1/2πr²), is incorrect for area as it would suggest a halved area, which doesn't apply in this context. Thus, A = πr² is the clear and direct formula for calculating the area of a circle