Why does this formula hold? We can understand it this way: first, cut the sphere into countless slices along the radius, and each slice is a circle. Then, the surface area of the sphere is equal to the sum of the areas of all circular sheets.

The area of each circular thin plate can be expressed by the formula A=πr? Where r is the radius of the circle. Because the sphere is cut along the radial direction, the radius of each piece is r, so the area of each piece is A=πr? .

Next, let's calculate the sum of the areas of all slices. Because the sphere is a geometric body in three-dimensional space, we can cut the sphere into countless slices along the radius and then calculate the sum of the areas of these slices. Since the area of each piece of paper is A=πr? So the surface area s of the sphere is: S=4πr? .

Here, 4πr? Represents the area of each slice multiplied by the number of slices. Since the sphere is composed of infinite slices, we can use 4πr? To represent the surface area of a sphere.

It is worth noting that this formula only applies to spheres. For other geometries, such as cylinders and cones, their surface area formulas are different. The surface area formula of sphere is a very important formula in mathematics, which is widely used in physics, engineering, computer graphics and other fields.

Mastering the surface area formula of a sphere can help us to calculate the surface area of a sphere quickly in practical problems. For example, when making spherical objects, the required material area can be calculated according to the radius of the sphere; This formula can be used to simplify the calculation when calculating the surface area difference between a sphere and other geometric bodies.

In a word, the formula of sphere surface area is a basic and important mathematical formula. By understanding the derivation process, we can better grasp this formula and use it flexibly in practical problems.

At the same time, mastering this formula is also helpful to improve our mathematical literacy and lay a solid foundation for further learning other mathematical knowledge. In daily life, we can also apply the surface area formula of a sphere to solve some practical problems, so as to realize the beauty and practicality of mathematics.