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    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: Early Transcendentals')
   15 ## EditionText1('5')
   16 ## AuthorText1('Stewart')
   17 ## Section1('6.3')
   18 ## Problem1('17')
   19 
   20 ## TitleText2('Calculus: Early Transcendentals')
   21 ## EditionText2('6')
   22 ## AuthorText2('Stewart')
   23 ## Section2('6.3')
   24 ## Problem2('')
   25 ## TitleText3('Calculus: Early Transcendentals')
   26 ## EditionText3('1')
   27 ## AuthorText3('Rogawski')
   28 ## Section3('6.4')
   29 ## Problem3('49')
   30 
   31 DOCUMENT();        # This should be the first executable line in the problem.
   32 
   33 loadMacros(
   34 "PG.pl",
   35 "PGbasicmacros.pl",
   36 "PGchoicemacros.pl",
   37 "PGanswermacros.pl",
   38 "PGauxiliaryFunctions.pl"
   39 );
   40 
   41 TEXT(beginproblem());
   42 $showPartialCorrectAnswers = 1;
   43 
   44 $a=random(1, 3,1);
   45 $b=random($a+1,8,1);
   46 $c=random($b+1,9,1);
   47 $soln = 2*$PI*($c*$b**3/3-$b**4/4-$c*$a**3/3+$a**4/4);
   48 
   49 TEXT(EV2(<<EOT));
   50 
   51 Find the volume of the solid obtained by rotating the region bounded by the
   52 curves
   53 \[ y=x^2, \quad  x = $a, \quad x = $b,\quad\text{and} \quad y=0 \]
   54 about the line \( x=$c \).
   55 $BR
   56 $BR
   57 Volume = \{ans_rule( 25) \}
   58 EOT
   59 ANS(num_cmp($soln));
   60 
   61 ENDDOCUMENT();        # This should be the last executable line in the problem.