What is the surface area formula for a sphere?

The surface area of a sphere is calculated using the formula S.A. = 4πr², where "r" represents the radius of the sphere. This formula arises from the geometric properties of a sphere and can be derived through calculus, considering the concept of integrating the circumference of a circle around an axis.

The factor of 4 comes from the fact that the surface area covers the entire outer layer of the sphere, and πr² is the area of a circle, which relates to how the sphere is constructed from infinitely many circular slices stacked together. This gives the formula its specific form, indicating that the area increases with the square of the radius, which aligns with how surface area intuitively scales with size.

This understanding of the surface area formula is essential in various applications, such as physics and engineering, where calculating the surface properties of spherical objects is necessary.