Question

the surface area of a sphere is calculated with which formula?
a. $4\pi r^{2}$
b. $2\pi r^{2}$
c. $2\pi r^{3}$
d. $\pi r^{2}$

Explanation:

Step1: Recall surface area formula

The formula for the surface area of a sphere is \(S = 4\pi r^{2}\), where \(r\) is the radius of the sphere.

Step2: Analyze each option

• Option a: \(4\pi r^{2}\) matches the formula.
• Option b: \(2\pi r^{2}\) is not the formula for sphere's surface area.
• Option c: \(2\pi r^{3}\) has the wrong power of \(r\) (volume - related form has \(r^{3}\) but this is not surface - area).
• Option d: \(\pi r^{2}\) is the area formula for a circle.

Answer:

A. \(4\pi r^{2}\)