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

The formula for the surface area of a sphere is derived from the relationship between its radius and the dimensions of the surface it encompasses. The surface area is given by the expression 4 times pi times the radius squared.

This formula can be understood by considering that the radius is a key dimension of the sphere that dictates the overall area covered by its surface. Pi is a constant that relates the circumference of a circle to its diameter, which comes into play when calculating the area of three-dimensional objects like spheres. Specifically, the formula shows that as the radius increases, the surface area grows with the square of the radius, highlighting how rapidly the surface area expands as the sphere gets larger.

In contrast, the other choices either reduce the power of the radius or incorrectly incorporate the diameter, demonstrating a misunderstanding of how surface area scales with radius in a spherical shape. The correct answer succinctly captures the relationship essential to calculating the surface area, affirming that for any given radius, the surface area can be reliably determined using that specific formula.