How do we calculate the area of the pupil given the radius?

The correct choice for calculating the area of a circle, such as the pupil, is given by the formula A = πr². This formula is derived from the geometric principles governing circles, where "A" represents the area, "π" (pi) is a constant approximately equal to 3.14159, and "r" is the radius of the circle.

The area of a circle is determined by squaring the radius, which gives the proportion of the area relative to the radius squared, and then multiplying that by π. This relationship is fundamental in geometry, allowing us to accurately describe the size of circular shapes.

Other options do not represent the area of a circle correctly. For example, one choice calculates the circumference of a circle (which is not the area), while others do not apply the principles of circle geometry appropriately either through incorrect mathematical constructs or by omitting critical components of the formula.