What is the formula for the area of a circle?

The formula for the area of a circle is given by ( A = \pi r^2 ). In this formula, ( A ) represents the area, ( \pi ) (approximately 3.14) is a constant that represents the ratio of the circumference of any circle to its diameter, and ( r ) stands for the radius of the circle, which is the distance from the center of the circle to any point on its circumference.

This formula derives from the concept of calculating the space contained within the circle. The area can be visualized as the total amount of flat space that is contained inside the circle's boundary. By squaring the radius (which gives ( r^2 )) and then multiplying that by ( \pi ), you effectively account for the curvature and shape of the circle in your area calculation.

Other formulas listed in the options relate to different geometric figures or calculations. For instance, the formula for the area of a rectangle uses ( A = bh ), where ( b ) is the base and ( h ) is the height. The volumetric formula ( V = \frac{1}{3} \text{(area of base)} \times \text{(height)} \