View of /trunk/rochester_problib/setIntegrals23Work/eva6_1.pg

    1 #DESCRIPTION
    2 #  Integration
    3 #  Application-based
    4 #  Physics--Work.
    5 #ENDDESCRIPTION
    6 
    7 #KEYWORDS('Integration', 'Physics', 'Applications')
    8 
    9 DOCUMENT();        # This should be the first executable line in the problem.
   10 
   11 loadMacros(
   12 "PG.pl",
   13 "PGbasicmacros.pl",
   14 "PGchoicemacros.pl",
   15 "PGanswermacros.pl",
   16 "PGauxiliaryFunctions.pl"
   17 );
   18 
   19 TEXT(&beginproblem);
   20 $showPartialCorrectAnswers = 1;
   21 
   22 #Here we ensure that the height of the tank is always greater than the depth of
   23 #the water
   24 $c1 = random(5,12,1);
   25 $c2 = $c1 ;
   26 while ($c1== $c2) {
   27     $c2 = random(1,11,1);
   28     }
   29 @cs =($c1,$c2);
   30 @sortedcs = num_sort(@cs);
   31 $C = $sortedcs[0];
   32 $A = $sortedcs[1];
   33 $b = random(3,20,1) ;
   34 $D = random(1450,1550,10);
   35 $pi = 4*arctan(1);
   36 
   37 BEGIN_TEXT
   38 A tank in the shape of an inverted right circular cone has height \( $A \) meters and
   39 radius \($b \) meters. It is filled with \($C \) meters of hot chocolate. $BR
   40 Find the work required to empty the tank by pumping the hot chocolate over the
   41 top of the tank. Note: the density of hot chocolate is
   42 \(\delta =  $D kg/m^3 \)
   43 $BR
   44 \{ans_rule(45)\}
   45 END_TEXT
   46 
   47 $answer = 9.8*$D*$pi*($b/$A)**2*( ($A**4)/12 - .5*$A**2*($A-$C)**2 + (2/3)*$A*($A-$C)**3 -.25*($A-$C)**4)  ;
   48 &ANS(std_num_cmp($answer));
   49 ENDDOCUMENT();        # This should be the last executable line in the problem.