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Fri Jun 9 20:01:08 2006 UTC (6 years, 11 months ago) by jjholt
File size: 1043 byte(s)
Added/fixed tags.


    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
24 "PG.pl",
25 "PGbasicmacros.pl",
26 "PGchoicemacros.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


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