View of /trunk/NationalProblemLibrary/OSU/accelerated_calculus_and_analytic_geometry_i/hmwk9/prob9.pg

    1 ## DESCRIPTION
    2 ##   Solid of Revolution Application
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('Solid', 'Revolution', 'Application')
    6 ## Tagged by nhamblet
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Applications of Integration')
   10 ## DBsection('Solids of Revolution')
   11 ## Date('5/20/2000')
   12 ## Author('Zig Fiedorowicz')
   13 ## Institution('Ohio State')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('Ellis & Gullick')
   17 ## Section1('8.1')
   18 ## Problem1('')
   19 
   20 DOCUMENT();
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGauxiliaryFunctions.pl"
   28 );
   29 
   30 $showPartialCorrectAnswers = 1;
   31 if (!($studentName =~ /PRACTICE/)) {
   32 $seed = random(1,4,1);
   33 if ($studentName =~ /VINCE VERSION1/) {$seed = 1;}
   34 if ($studentName =~ /VINCE VERSION2/) {$seed = 2;}
   35 if ($studentName =~ /VINCE VERSION3/) {$seed = 3;}
   36 if ($studentName =~ /VINCE VERSION4/) {$seed = 4;}
   37 SRAND($seed);}
   38 
   39 
   40 $bb = random(2,5);
   41 $aa = $bb+random(1,3);
   42 $aa = 10*$aa;
   43 $a2 = $aa*$aa;
   44 $bb = 10*$bb;
   45 $b2 = $bb*$bb;
   46 
   47 TEXT(beginproblem());
   48 BEGIN_TEXT
   49 As viewed from above, a swimming pool has the shape of the ellipse
   50 \[\frac{x^2}{$a2}+\frac{y^2}{$b2}=1\]
   51 The cross sections perpendicular to the ground and parallel to the \(y\)-axis
   52 are squares. Find the total volume of the pool. (Assume the units of length and
   53 area are feet and square feet respectively. Do not put units in your answer.)
   54 $BR
   55 \(V\) = \{ ans_rule()\}
   56 $PAR
   57 
   58 END_TEXT
   59 
   60 ANS(num_cmp((16/3)*$b2*$aa));
   61 
   62 ENDDOCUMENT();