Question

1. what is the formula for the volume of a sphere? a. \\( \frac { 4 } { 3 } \pi r ^ { 3 } \\) b. \\( \pi r ^ { 2 } \\) c. \\( 2 \pi r \\) d. \\( \frac { 3 } { 4 } \pi r ^ { 2 } \\)

Explanation:

Step1: Recall the formula for the volume of a sphere

The volume \(V\) of a sphere with radius \(r\) is given by \(V = \frac{4}{3}\pi r^{3}\).

Step2: Analyze other options

• Option b: \(\pi r^{2}\) is the formula for the area of a circle (not volume).
• Option c: \(2\pi r\) is the formula for the circumference of a circle (not volume).
• Option d: \(\frac{3}{4}\pi r^{2}\) is not a standard formula related to the volume of a sphere.

Answer:

A. $\frac{4}{3}\pi r^{3}$