# Volume3

## A Question That Provides Credit Only When All Answers Are Correct

This PG code shows how to ask students to set up a volume of solids of revolution integral in which all parts must be correct for the student to receive any credit.

PG problem file Explanation

Problem tagging:

DOCUMENT();

"PGstandard.pl",
"MathObjects.pl",
"PGunion.pl",
);

TEXT(beginproblem());

$showPartialCorrectAnswers = 1;  Initialization: We install the standard problem grader, which is an all-or-nothing grader. Context("Numeric"); Context()->variables->are( x=>"Real", dx=>"Real", y=>"Real", dy=>"Real" );$f = Compute("x");
$g = Compute("x^2");$upper = Real("1");
$lower = Real("0"); # answers below are intentionally wrong$int = Compute("( pi x - pi x^2 ) dx");
$vol = Compute("pi"); # # Display the answer blanks properly in different modes # Context()->texStrings; if ($displayMode eq 'TeX') {
$integral = 'Volume = $$\displaystyle' . '\int_{'. ans_rule(4). '}^{'. ans_rule(4). '}'. ans_rule(30). ' = '. ans_rule(10). '$$'; } else {$integral =
BeginTable(center=>0).
Row([
'Volume = $$\displaystyle\int$$',
ans_rule(4).$BR.$BR.
ans_rule(4),
ans_rule(30).$SPACE.' = '.$SPACE.
ans_rule(10),
],separation=>2).
EndTable();
}
Context()->normalStrings;


Setup: Notice that we use ans_rule(width) for all of the answer blanks.

Context()->texStrings;
BEGIN_TEXT
Set up and evaluate an integral for the volume
of the solid of revolution obtained by rotating
the region bounded by $$y = f$$ and $$y = g$$
about the $$x$$-axis.
$BR$BR
$integral END_TEXT Context()->normalStrings;  Main Text: The standard problem grader automatically provides a message to students that says the grading will be all or nothing. ANS($upper->cmp() );
ANS( $lower->cmp() ); ANS($int->cmp()
Formula("pi x - pi x^2 dx") => "Don't forget to multiply every
term in the integrand by dx",
Formula("pi x - pi x^2") => "Don't forget the differential dx",
Formula("(pi x^2 - pi x)*dx") => "Is the parabola above the line?",
Formula("pi x^2 - pi x") => "Is the parabola above the line?",
))
);
ANS( \$vol->cmp() );


Context()->texStrings;
BEGIN_SOLUTION
Solution explanation goes here.
END_SOLUTION
Context()->normalStrings;

COMMENT('MathObject version.  Gives full credit only