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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 67 "    Ein Kelchglas, gegeben durch einen \+
\326ffnungswinkel und der H\366he," }}{PARA 0 "" 0 "" {TEXT -1 60 "   \+
 wird teilweise gef\374llt, z.B. mit 1/3 des Gesamtvolumens," }}{PARA 
0 "" 0 "" {TEXT -1 31 "    gesucht ist die F\374llh\366he h2" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 44 "grad:=x->180*x/Pi:       bogen:=x->Pi*x/1
80:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 44 "h1:=20:                      # Gesamth\366he
 h1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "o_winkel:=90:       \+
         # \326ffnungswinkel" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 48 "r1:=h1* evalf(tan (bogen( o_winkel/2)),6):      " }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "V_kegel:=evalf(1/3*Pi*h1*r1^2,6):" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "V_Anteil:= V_kegel/3:    \+
          # Drittel" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "h_te
mp:=solve(r1/r2=h1/h2,  h2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 35 "g:=V_Anteil-1/3*Pi*h_temp*(r2)^2=0:" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 11 "evalf(g,8):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 36 "g1:=solve(g,r2): r_Teilkegel:=g1[1]:" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 28 "h2:=subs(r2=g1[1] , h_temp):" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 22 "Fuellhoehe:=evalf(h2);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%+FuellhoeheG^$$!+JEhLp!\"*$!+Op$4?\"!\")" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 5 "Probe" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
45 "V_anteil:=evalf(1/3*Pi*h2*(r_Teilkegel)^2,8):" }}}{EXCHG {PARA 2 "
" 1 "" {TEXT -1 1 "\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "res
tart;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 73 "    Ein Kelchglas, gegeb
en durch die H\366he und den Radius des Deckkreises," }}{PARA 0 "" 0 "
" {TEXT -1 60 "    wird teilweise gef\374llt, z.B. mit 1/3 des Gesamtv
olumens," }}{PARA 0 "" 0 "" {TEXT -1 28 "    gesucht ist die F\374llh
\366he" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "grad:=x->180*x/Pi:       \+
bogen:=x->Pi*x/180:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "h:=8
: r:=4:" }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 36 "alpha:=2*evalf(grad(arctan(r/h)),6);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&alphaG$\"'-8`!\"%" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 31 "Volumen:=evalf(1/3*Pi*h*r^2,6);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%(VolumenG$\"'TS8!\"$" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 0 "" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 46 " V_Anteil:= Volumen/2:                # H\344lfte" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 " h1:=r1/ evalf(tan (bogen(a
lpha/2)),4):     " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " g:=V_
Anteil=1/3*Pi*h1*(r1)^2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 
" evalf(g,8):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 " g1:=solve
(g,r1): r_Teilkegel:=g1[1]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
57 " h_Teilkegel:=r_Teilkegel/ evalf(tan (bogen(alpha/2)),4):" }}}
{EXCHG {PARA 2 "" 0 "" {TEXT -1 1 "\n" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 57 "Kelch aus Papier basteln,   Radius  d
es Kreises bestimmen" }}{PARA 0 "" 0 "" {TEXT -1 7 "Radius:" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 56 "Mantellinie:=r/evalf(sin(bogen(alpha/2)),
4);   #  Radius" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,M
antellinieG$\"+aTaU*)!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "Winke
l:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "b:=evalf(  2*Pi*r,4); " }
{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG$\"%9D!\"#" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "auszuschneidenderWinkel:=360
-solve( b/(2*Pi*Mantellinie  )=winkel/360,winkel);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%8auszuschneidenderWinkelG$\"+B\\D*)>!\"(" }}}
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