The lateral surface area of a cylindrical tube with a height of 6 cm is $48\pi$ square centimeters. In cubic centimeters, what is the tube's volume? Express your answer in terms of $\pi$.
The lateral surface area of a cylinder is given by the formula $LSA = 2\pi rh$, where $r$ is the radius and $h$ is the height. I can plug in the given values of $LSA$ and $h$ and solve for $r$. So I have $48\pi = 2\pi r(6)$, which simplifies to $r = 4$. The volume of a cylinder is given by the formula $V = \pi r^2 h$. I can plug in the values of $r$ and $h$ that I found and calculate $V$. So I have $V = \pi (4)^2 (6)$, which simplifies to $V = 96\pi$. 