Question

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

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 each option

• Option A: \(4\pi r^{3}\) is incorrect.
• Option B: \(\frac{4}{3}\pi r^{3}\) is correct as per the formula.
• Option C: \(\frac{3}{4}\pi r^{3}\) is incorrect.
• Option D: \(\pi r^{2}h\) is the formula for the volume of a cylinder (where \(h\) is the height), not a sphere.

Answer:

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