View of /trunk/NationalProblemLibrary/UVA-Stew5e/setUVA-Stew5e-C06S03-VolumesShells/6-3-19.pg

    1 ## DESCRIPTION
    2 ## Calculus: Volumes by Cylindrical Shells
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('calculus', 'integrals', 'volumes', 'cylindrical shells')
    6 ## Tagged by XW
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Applications of Integration')
   10 ## DBsection('Volumes by Cylindrical Shells')
   11 ## Date('6/5/2005')
   12 ## Author('Jeff Holt')
   13 ## Institution('UVA')
   14 ## TitleText1('Calculus')
   15 ## EditionText1('5e')
   16 ## AuthorText1('Stewart')
   17 ## Section1('6.3')
   18 ## Problem1('19')
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGauxiliaryFunctions.pl"
   28 );
   29 
   30 TEXT(beginproblem());
   31 $showPartialCorrectAnswers = 1;
   32 
   33 $a=random(2, 8,1);
   34 $soln = $PI*8*(-3+4*$a)/3;
   35 
   36 TEXT(EV2(<<EOT));
   37 
   38 Find the volume of the solid obtained by rotating the region bounded by the
   39 given curves about the specified line.
   40 \[ y=\sqrt{x - 1 }, \quad y = 0 , \quad x = 5;  \]
   41 about the line \(y=$a\).
   42 
   43 $BR
   44 Volume = \{ans_rule( 25) \}
   45 $BR
   46 EOT
   47 ANS(num_cmp($soln));
   48 
   49 ENDDOCUMENT();        # This should be the last executable line in the problem.