View of /trunk/NationalProblemLibrary/Union/setIntSurfaceArea/ur_in_27_1.pg

    1 ## DESCRIPTION
    2 ##   Calculate a Surface Area of a Solid of Revolution
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('Surface Area', 'Solid of Revolution', 'Rotate Curve')
    6 ## Tagged by nhamblet
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Applications of Integration')
   10 ## DBsection('Solids of Revolution')
   11 ## Date('8/23/07')
   12 ## Author('')
   13 ## Institution('Union')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 ## TitleText2('Calculus: Early Transcendentals')
   20 ## EditionText2('1')
   21 ## AuthorText2('Rogawski')
   22 ## Section2('6.3')
   23 ## Problem2('43')
   24 
   25 DOCUMENT();        # This should be the first executable line in the problem.
   26 
   27 loadMacros(
   28   "PGstandard.pl",
   29   "PGunion.pl",            # Union College utilities
   30   "MathObjects.pl",
   31   "PGcourse.pl",           # Customization file for the course
   32 );
   33 
   34 TEXT(beginproblem());
   35 
   36 ###################################
   37 # Setup
   38 
   39 $a = random(2,6,1);
   40 $b = random(1,9,1);
   41 
   42 $curve=Formula("$a x^3");
   43 $left=0;
   44 $right=$b;
   45 
   46 ###################################
   47 # Main text
   48 
   49 Context()->texStrings;
   50 BEGIN_TEXT
   51 
   52 Find the area of the surface obtained by rotating the curve
   53 \[y = $curve\]
   54 from \(x = $left\) to \(x = $right\) about the \(x\)-axis.
   55 $PAR
   56 
   57 The area is \{ans_rule(50)\} square units.
   58 
   59 END_TEXT
   60 Context()->normalStrings;
   61 
   62 ###################################
   63 # Answers
   64 
   65 $showPartialCorrectAnswers = 1;
   66 Context()->flags->set(tolerance => .001);
   67 Context()->flags->set(reduceConstants=>0);
   68 
   69 $answer = "(pi/(27*$a))*((1+9*$a*$a*$b**4)**1.5 -1)";
   70 ANS(Compute($answer)->cmp);
   71 
   72 ###################################
   73 
   74 
   75 COMMENT('MathObject version');
   76 ENDDOCUMENT();