## 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.