Question

1. what is the formula for the volume of a sphere?

a. $\pi r^{2}h$
b. $4\pi r^{3}$
c. $\frac{3}{4}\pi r^{3}$
d. $\frac{4}{3}\pi r^{3}$

Explanation:

The volume formula for a sphere is derived from integral calculus or can be memorized as a standard geometric formula. Let's analyze each option:

• Option a: \(\pi r^{2}h\) is the formula for the volume of a cylinder.
• Option b: \(4\pi r^{3}\) is not the correct formula for the volume of a sphere. The surface - area formula of a sphere is \(4\pi r^{2}\).
• Option c: \(\frac{3}{4}\pi r^{3}\) is not a standard geometric volume formula for common 3 - D shapes.
• Option d: The formula for the volume of a sphere with radius \(r\) is \(V=\frac{4}{3}\pi r^{3}\).

Answer:

D. \(\frac{4}{3}\pi r^{3}\)