View of /trunk/NationalProblemLibrary/272/setStewart15_6/ur_vc_10_1.pg

    1 ## DESCRIPTION
    2 ##   Compute Surface Area
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('Multiple Integral', 'Surface Area')
    6 ## Tagged by nhamblet
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Multiple Integrals')
   10 ## DBsection('Surface Area')
   11 ## Date('6/2/2000')
   12 ## Author('Joseph Neisendorfer')
   13 ## Institution('University of Rochester')
   14 ## TitleText1('Calculus: Early Transcendentals')
   15 ## EditionText1('5')
   16 ## AuthorText1('Stewart')
   17 ## Section1('15.6')
   18 ## Problem1('')
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros("PG.pl",
   23            "PGbasicmacros.pl",
   24            "PGchoicemacros.pl",
   25            "PGanswermacros.pl",
   26            "PGauxiliaryFunctions.pl");
   27 
   28 TEXT( beginproblem() );
   29 $showPartialCorrectAnswers = 1;
   30 
   31 $a = random( 1, 5, 1 );
   32 $b = random( 1, 5, 1 );
   33 $c = random( 1, 5, 1 );
   34 $d = random( 1, 5, 1 );
   35 
   36 $d_squared = $d**2;
   37 
   38 $ans = $PI * $d**2 * sqrt( 1 + $a**2 + $b**2 );
   39 
   40 BEGIN_TEXT
   41 Find the surface area of the part of the plane \( $a x + $b y + z = $c \) that
   42 lies inside the cylinder \( x^{2} + y^{2} = $d_squared \).
   43   $PAR
   44 \{ans_rule(40)\}
   45 END_TEXT
   46 
   47 ANS(num_cmp($ans));
   48 
   49 ENDDOCUMENT();        # This should be the last executable line in the problem.