##DESCRIPTION
## Given a wire, cut it to form a circle and square of minimum area 
##ENDDESCRIPTION


## Tagged by sawblade

## DBsubject(Algebra)
## DBchapter(Quadratic equations and functions)
## DBsection(Applications and models)
## Date(6/3/2002)
## Level(3)
## TitleText1('College Algebra')
## AuthorText1('Stewart, Redlin, Watson')
## EditionText1('3')
## Section1('3.3')
## Problem1('72')
## KEYWORDS('algebra', 'word problem' 'cutting wire', 'quadratic')

DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
  "PGstandard.pl",
  "PGchoicemacros.pl",
  "PGcourse.pl"
);

TEXT(beginproblem());
$showPartialCorrectAnswers = 1;

$length = random(20,100,3);

$ans = (2*$length/16)/(2*(1/(4*$PI) +1/16));


BEGIN_TEXT;
You have a wire that is $length cm long.  You wish to cut it into two pieces.
One piece will be bent into the shape of a square.  The other piece 
will be bent into the shape of a circle.  Let A represent
the total area of the square and the circle.  What is the circumference of the
circle when A is a minimum?
$BR$BR
The circumference of the circle is  \{ans_rule(10)\} cm.
END_TEXT;

ANS(num_cmp($ans, mode=>"strict"));


ENDDOCUMENT();        # This should be the last executable line in the problem.

