How do you calculate the area of a circle?

To calculate the area of a circle, the formula used is ( A = \pi r^2 ), where ( A ) represents the area and ( r ) is the radius of the circle. This formula is derived from the relationship between the radius and the circular shape. The radius is half the diameter, and using it in the formula allows you to determine how much space is enclosed within the circle's boundary.

The concept behind this formula involves integrating infinitesimally small slices of the circle and summing them up to determine the total area. Since the area is proportional to the square of the radius, any increase in the radius will lead to a greater increase in the area. Hence, the correct choice reflects this principle accurately, providing a clear and precise way to obtain the area of a circle using its radius.

The other choices relate to different properties or measures of the circle, such as its circumference or volume, rather than directly addressing the area calculation. Hence, only the formula involving the radius squared accurately describes the method for finding the area.