To calculate the surface area of a sphere, which formula is used?

To calculate the surface area of a sphere, which formula is used?

• A. SA = 2πr²
• B. SA = πr²
• C. SA = 4πr²
• D. SA = 4πr³

Answer: (C)

The surface area of a sphere is calculated using the formula \( SA = 4\pi r^2 \). This formula accounts for the entire outer surface of a sphere, where \( r \) is the radius of the sphere. In this formula, the \( 4\pi \) constant represents the geometric relationship that arises from the properties of three-dimensional shapes. The \( r^2 \) term indicates that the surface area increases with the square of the radius, meaning that as the radius increases, the surface area grows significantly. This relationship is fundamental in geometry, especially when dealing with spheres, which are perfectly symmetrical shapes. The other options listed do not correctly represent the surface area of a sphere. For instance, both the formulas that incorporate \( r^3 \) relate to volume rather than surface area, and the formula \( SA = 2\pi r^2 \) does not correspond to any common geometric property of a sphere. Therefore, \( SA = 4\pi r^2 \) is the appropriate formula for calculating the surface area of a sphere.

The surface area of a sphere is calculated using the formula ( SA = 4\pi r^2 ). This formula accounts for the entire outer surface of a sphere, where ( r ) is the radius of the sphere.

In this formula, the ( 4\pi ) constant represents the geometric relationship that arises from the properties of three-dimensional shapes. The ( r^2 ) term indicates that the surface area increases with the square of the radius, meaning that as the radius increases, the surface area grows significantly.

This relationship is fundamental in geometry, especially when dealing with spheres, which are perfectly symmetrical shapes. The other options listed do not correctly represent the surface area of a sphere. For instance, both the formulas that incorporate ( r^3 ) relate to volume rather than surface area, and the formula ( SA = 2\pi r^2 ) does not correspond to any common geometric property of a sphere. Therefore, ( SA = 4\pi r^2 ) is the appropriate formula for calculating the surface area of a sphere.