\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} An oil tank has the shape of a
cylinder whose diameter is 4 feet. It is mounted so that the axis of
the cylinder is horizontal (the circular cross-sections of the
cylinder are vertical). If the depth of the water is 3 feet, what
percentage of the total capacity of the tank is filled?

\medskip

\noindent After drawing a picture and setting up this problem, solve
it three ways:

\medskip

\noindent a) Use elementary geometry (compare areas of circular
sectors).

\medskip

\noindent b) Express the answer in terms of a definite integral, then
obtain an approximate numerical value for the integral using the {\tt
fnInt(} function on your calculator.

\medskip

\noindent c) Evaluate the integral in b) exactly in terms of
elementary functions using a trig substitution, then obtain
approximate numerial values for these functions using your calculator.

\vfil\eject\end

