Question

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

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

b. $4pi r^{3}$

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

d. $pi r^{2}h$

Explanation:

Step1: Recall volume formula for sphere

The volume \(V\) of a sphere with radius \(r\) is derived from integral calculus (by integrating infinitesimal volume elements over the spherical shape). The standard formula is \(V = \frac{4}{3}\pi r^{3}\).

Step2: Analyze other options

• Option B: \(4\pi r^{3}\) is incorrect. The coefficient should be \(\frac{4}{3}\), not \(4\).
• Option C: \(\frac{3}{4}\pi r^{3}\) has the wrong coefficient.
• Option D: \(\pi r^{2}h\) is the volume formula for a cylinder (where \(h\) is the height of the cylinder), not a sphere.

Answer:

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