Cooper Section $8\mathrm{.}7\backslash$#$11$

A piece of PVC pipe which is open at both ends encloses a volume $\backslash ($ V$($r$,$ l$)=\backslash$pi r$^\{2\}$ l $\backslash ),$ where $\backslash ($ r $\backslash )$ is the radius of the pipe and $\backslash ($ l $\backslash )$ is its length. Suppose for a fixed length $\backslash ($ l $\backslash )$ we vary the radius $\backslash ($ r $\backslash )$ of the pipe.

a$.$ What is the rate of change of volume with respect to radius?

rate of change $\backslash (=\backslash )$

b$.$ What quantity does the formula for this rate give?

A$.$ cross$-$sectional area

B$.$ surface area

C$.$ diameter squared

D$.$ diameter

E$.$ average rate of increase of volume

F$.$ None of the above