Question

the formula for the volume of a sphere is:
a. $\frac{4}{3}\pi r^{3}$
b. $\pi d^{2}h$
c. $\frac{1}{2}\pi r^{2}h$
d. $\pi r^{2}h$

Explanation:

Step1: Recall the volume formula for a sphere

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

Step2: Analyze option b

The formula \(\pi d^{2}h\) is not a standard geometric volume formula.

Step3: Analyze option c

The formula \(\frac{1}{2}\pi r^{2}h\) is not the volume formula for a sphere. It might be related to some non - standard or incorrect derivation for a different shape.

Step4: Analyze option d

The formula \(\pi r^{2}h\) is the volume formula for a cylinder (where \(r\) is the radius of the base and \(h\) is the height), not for a sphere.

Answer:

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