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 the formula for the volume of a sphere

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

Step2: Substitute the given radius into the formula

The radius \( r \) of the sphere is given as 6 units. Substituting \( r = 6 \) into the formula \( V=\frac{4}{3}\pi r^{3} \), we get \( V=\frac{4}{3}\pi(6)^{3} \).

Answer:

\(\boldsymbol{\frac{4}{3}\pi(6)^{3}}\) (corresponding to the second option: \(\frac{4}{3}\pi(6)^{3}\))