FTCE General Knowledge Math Practice Test

What formula is used to determine the total surface area of a sphere?

1. (4/3)(3.14)(r^3)

2. 3.14(r^2)(h)

3. 2(3.14)(r^2)

4. 4(3.14)(r^2)

The correct answer is: 4(3.14)(r^2)

The total surface area of a sphere is defined by the formula \(4\pi r^2\), where \(r\) represents the radius of the sphere. This formula comes from the geometric principles related to spheres and accounts for the entire area that covers the surface. The choice given as correctly identifying the formula uses \(4\) multiplied by \(\pi\) (approximately \(3.14\)) and the square of the radius, which effectively captures the entire surface area of a sphere. The derivation of this formula considers the symmetry and uniform curvature of a sphere, leading to the conclusion that this is the correct representation of the surface area. The other choices do not represent the surface area of a sphere. Some of them relate to different geometric shapes or concepts, such as volume or surface area of cylinders, which do not apply in this context. This further solidifies that the chosen formula correctly describes the total surface area of a sphere.