\ANG{
%
%%\item
%
\begin{minipage}[t]{8cm}


Die nebenstehende Figur rotiert um die Achse $a$.
Bestimmen Sie f"ur den Rotationsk"orper 
\begin{enumerate}
\item{das Volumen $V$}
\item{die Oberfl"ache $O$}
\end{enumerate}
\end{minipage}
\hglue 10 pt
\begin{minipage}[t]{8 cm}
\beginpicture

\setcoordinatesystem units <0.5mm,0.5mm> point at 40 60
\setplotarea x from -40 to 40, y from -20 to 70
\footnotesize

\setlinear
\setplotsymbol ({\fontsize{12}{1ex}\selectfont .}) \plotsymbolspacing 0.2pt

%Kontur
\plot  20   0    30   0    30  30   / %rechts unten
\plot -20   0   -30   0   -30  30   / %links  unten
\plot -40  30    40  30     0  60   -40  30 / %Dach
\circulararc 180 degrees from 20  0  center at 0 0
%Achse
\setdashpattern <2mm,1mm,0.5mm,1mm>
\plot 0 -10  0 65 /
% Beschriftung
\setsolid
\setplotsymbol ({\fontsize{5}{1ex}\selectfont .}) \plotsymbolspacing 0.2pt
\arrow <1mm> [0.5,1.0] from 7  -9 to 0 -9
\arrow <1mm> [0.5,1.0] from 13 -9 to 20 -9
\put {$l$}  at 10 -9                          % l unten
\plot 20  0   20 -12 /
\betweenarrows {\makebox[10pt]{$1,5 l$}}       from   0  -18  to  30 -18
\plot 30  0   30 -21 /

\betweenarrows {$2l$}             from -40  63   to   0  63
\plot -40 30    -40 66 /
\betweenarrows {$1,5l$}             from  43   0   to  43  30
\plot 30  0 46  0 /
\plot 40 30 46 30 /
\betweenarrows {\makebox[0pt]{$1,5l$}} from  43  30   to  43  60
\plot  0 60 46 60 /
\put {a} at 3 65

\endpicture


\end{minipage}

}
\LSG{
\begin{enumerate}
\item
$V={1 \over 3} (2l)^2\pi\cdot 1{,}5 l + (1{,}5l)^2\pi\cdot 1{,}5l 
                                      - {1 \over 2}\cdot {4\over 3} \pi l^3=
  {113 \over 24} \pi l^3$
\item 
L"ange der Mantellinie: $m=2{,}5l$. 

Oberfl"ache:

$O=  {1\over2}m\cdot2\pi\cdot 2l+ 1{,}5l\cdot 2\pi\cdot 1{,}5 l+(\pi(2l)^2
    -\pi l^2 + {1 \over 2} 4\pi l^2 = 14{,}5\pi l^2$
\end{enumerate}        
}
