Write the Word or Phrase That Best Completes Each Statement $\mathrm { V }$

question 100

Essay

Write the word or phrase that best completes each statement or answers the question.
-The volume $\mathrm { V }$ (in cubic inches) of a cylindrical pipe with length 12 inches is given by $\mathrm { V } ( \mathrm { r } ) = 12 \pi \mathrm { r } ^ { 2 }$ , where $\mathrm { r }$ is the radius of the piston (in inches). If the radius is increasing with time $t$ (in minutes) according to the formula $r ( t ) = \frac { 1 } { 6 } t ^ { 2 } , t \geq 0$ , find the volume $V$ of the pipe as a function of the time $t$ .