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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')
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
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.pl",
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
45 $BR 46 EOT 47 ANS(num_cmp($soln));