Question

the radius of a sphere is 6 units. which expression represents the volume of the sphere, in cubic units? $\frac{3}{4}\pi(6)^2$ $\frac{4}{3}\pi(6)^3$ $\frac{3}{4}\pi(12)^2$ $\frac{4}{3}\pi(12)^3$

Explanation:

Step1: Recall sphere volume formula

The volume $V$ of a sphere is given by $V = \frac{4}{3}\pi r^3$, where $r$ is the radius.

Step2: Substitute radius $r=6$

Substitute $r=6$ into the formula: $V = \frac{4}{3}\pi (6)^3$

Step3: Match with options

Compare the derived expression to the given choices.

Answer:

$\boldsymbol{\frac{4}{3}\pi(6)^3}$ (the second option)