##Ellis and Gullick: section 8.1
##Final exam review
##Authored by Zig Fiedorowicz 5/20/2000
DOCUMENT();

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl"
);

$showPartialCorrectAnswers = 1;
if (!($studentName =~ /PRACTICE/)) {
$seed = random(1,4,1);
if ($studentName =~ /VINCE VERSION1/) {$seed = 1;}
if ($studentName =~ /VINCE VERSION2/) {$seed = 2;}
if ($studentName =~ /VINCE VERSION3/) {$seed = 3;}
if ($studentName =~ /VINCE VERSION4/) {$seed = 4;}
SRAND($seed);}


$bb = random(2,5);
$aa = $bb+random(1,3);
$aa = 10*$aa;
$a2 = $aa*$aa;
$bb = 10*$bb;
$b2 = $bb*$bb;

TEXT(&beginproblem);
BEGIN_TEXT
As viewed from above, a swimming pool has the shape of the ellipse
\[\frac{x^2}{$a2}+\frac{y^2}{$b2}=1\]
The cross sections perpendicular to the ground and parallel to the \(y\)-axis
are squares. Find the total volume of the pool. (Assume the units of length and
area are feet and square feet respectively. Do not put units in your answer.)
$BR
\(V\) = \{ ans_rule()\}
$PAR

This is similar to problem 47 in section 8.1 of the text.
END_TEXT

&ANS(num_cmp((16/3)*$b2*$aa));

ENDDOCUMENT();