FTCE Professional Education Practice Exam

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

1. 2πr²

2. 4πr²

3. πr²

4. 6πr²

The correct answer is: 4πr²

The formula for calculating the total surface area of a sphere is given by 4πr², where r represents the radius of the sphere. This formula arises from the geometric properties of spheres and involves integrating the circular areas that make up a sphere. To understand why 4πr² is used: the “4” in the formula indicates that you are accounting for all points of the sphere's surface area, while π relates to the circular cross-section of the sphere. Thus, when you consider a sphere as a three-dimensional object, the surface area increases as the square of the radius, and it is multiplied by 4 to accommodate the entire surface. This formula is crucial in various applications, including physics and engineering, where surface area calculations are often necessary for understanding phenomena involving spheres, like bubbles, planets, or even particles in various scientific fields. Overall, 4πr² succinctly captures the entire surface area for a sphere, making it the correct answer.