View of /trunk/NationalProblemLibrary/ASU-topics/setCalc2/tracogna30.pg

    1 ## DESCRIPTION
    2 ## Calculus: Parametric Equations: Surface Area
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('surface area')
    6 ## Tagged by jjh2b
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Parametric Equations and Polar Coordinates')
   10 ## DBsection('Arc Length and Surface Area')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('ASU')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 
   21 DOCUMENT();        # This should be the first executable line in the problem.
   22 
   23 loadMacros(
   24 "PG.pl",
   25 "PGbasicmacros.pl",
   26 "PGchoicemacros.pl",
   27 "PGanswermacros.pl",
   28 "PGauxiliaryFunctions.pl",
   29 "PGasu.pl"
   30 );
   31 
   32 TEXT(beginproblem());
   33 
   34 $a = random(2,8);
   35 
   36 
   37 $pi = 4*arctan(1);
   38 
   39 $ans = 16*$pi*$a**2/15;
   40 
   41 
   42 BEGIN_TEXT
   43 Find the area of the surface obtained by rotating the curve of
   44 parametric equations:
   45 \[ x = $a t - \frac{$a}{3} t^3, \; y = $a t^2,\; 0 \le t \le 1 \]
   46 about the $BITALIC x $EITALIC - axis.
   47   $PAR
   48   Surface Area  = \{ans_rule(40)\}
   49 END_TEXT
   50 
   51 ANS(num_cmp($ans));
   52 
   53 ENDDOCUMENT();        # This should be the last executable line in the problem.
   54