## DESCRIPTION ## Calculus: Parametric Equations: Surface Area ## ENDDESCRIPTION ## KEYWORDS('surface area') ## Tagged by jjh2b ## DBsubject('Calculus') ## DBchapter('Parametric Equations and Polar Coordinates') ## DBsection('Arc Length and Surface Area') ## Date('') ## Author('') ## Institution('ASU') ## TitleText1('') ## EditionText1('') ## AuthorText1('') ## Section1('') ## Problem1('') DOCUMENT(); # This should be the first executable line in the problem. loadMacros( "PG.pl", "PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", "PGauxiliaryFunctions.pl", "PGasu.pl" ); TEXT(beginproblem()); $a = random(2,8);$pi = 4*arctan(1); $ans = 16*$pi*$a**2/15; BEGIN_TEXT Find the area of the surface obtained by rotating the curve of parametric equations: $x = a t - \frac{a}{3} t^3, \; y = a t^2,\; 0 \le t \le 1$ about the$BITALIC x $EITALIC - axis.$PAR Surface Area = \{ans_rule(40)\} END_TEXT ANS(num_cmp(\$ans)); ENDDOCUMENT(); # This should be the last executable line in the problem.