What is the formula for the surface area of a sphere?

The surface area of a sphere is given by the formula 4πr², where r represents the radius of the sphere. This formula captures how the surface area is related to the radius, indicating that the surface area increases with the square of the radius.

To derive this formula, consider that a sphere consists of an infinite number of infinitesimally small flat pieces, each related to the radius. When calculating the area, the factor of 4 arises due to the geometric properties of a sphere, which is essentially a three-dimensional object that wraps around its center. The π in the formula reflects the relationship between the circumference and diameter, which is fundamental in circle-related calculations.

In contrast, the other formulas given correspond to different geometric shapes or configurations. The second option (2πr² + 2πrh) pertains to the surface area of a cylinder, considering both the curved surface and the top and bottom faces. The third option (πr² + πrl) is related to the surface area of a cone, which includes the area of its circular base and the lateral surface area. The fourth option (4/3πr³) is the formula for the volume of a sphere, not the surface area.

Understanding these