SolidsWW Flash Applet Sample Problem 3

Sample Problem 3 with solidsWW.swf embedded

This sample problem shows how to use this versatile applet.

A standard WeBWorK PG file with an embedded applet has six sections:

1. A tagging and description section, that describes the problem for future users and authors,
2. An initialization section, that loads required macros for the problem,
3. A problem set-up section that sets variables specific to the problem,
4. An Applet link section that inserts the applet and configures it, (this section is not present in WeBWorK problems without an embedded applet)
5. A text section, that gives the text that is shown to the student, and
6. An answer and solution section, that specifies how the answer(s) to the problem is(are) marked for correctness, and gives a solution that may be shown to the student after the problem set is complete.

The sample file attached to this page shows this; below the file is shown to the left, with a second column on its right that explains the different parts of the problem that are indicated above. A screenshot of the applet embedded in this WeBWorK problem is shown below:

There are other example problems using this applet:
solidsWW Flash Applet Sample Problem 1
solidsWW Flash Applet Sample Problem 2
And other problems using applets:
Derivative Graph Matching Flash Applet Sample Problem
USub Applet Sample Problem
trigwidget Applet Sample Problem
solidsWW Flash Applet Sample Problem 1
GraphLimit Flash Applet Sample Problem 2
Other useful links:
Flash Applets Tutorial
Things to consider in developing WeBWorK problems with embedded Flash applets

PG problem file	Explanation
##DESCRIPTION ## Solids of Revolution ##ENDDESCRIPTION ##KEYWORDS('Solids of Revolution') ## DBsubject('Calculus') ## DBchapter('Applications of Integration') ## DBsection('Solids of Revolution') ## Date('7/31/2011') ## Author('Barbara Margolius') ## Institution('Cleveland State University') ## TitleText1('') ## EditionText1('2011') ## AuthorText1('') ## Section1('') ## Problem1('') ########################################## # This work is supported in part by the # National Science Foundation # under the grant DUE-0941388. ##########################################	This is the tagging and description section of the problem. Note that any line that begins with a "#" character is a comment for other authors who read the problem, and is not interpreted by WeBWorK. The description is provided to give a quick summary of the problem so that someone reading it later knows what it does without having to read through all of the problem code. All of the tagging information exists to allow the problem to be easily indexed. Because this is a sample problem there isn't a textbook per se, and we've used some default tagging values. There is an on-line list of current chapter and section names and a similar list of keywords. The list of keywords should be comma separated and quoted (e.g., KEYWORDS('calculus','derivatives')).
DOCUMENT(); loadMacros( "PGstandard.pl", "AppletObjects.pl", "MathObjects.pl", );	This is the initialization section of the problem. The first executed line of the problem must be the DOCUMENT(); command. Note that every command must end with a semicolon. The loadMacros command loads information that works behind the scenes. For our purposes we can usually just load the macros shown here and not worry about things further.
TEXT(beginproblem()); $showPartialCorrectAnswers = 1; Context("Numeric"); $a = 2*random(2,6,1); $b = 2*$a; $xy = 'x'; $func1 = "x"; $func2 = "2*$a-x"; $xmax = Compute("2*$a"); $shapeType = 'poly'; $sides = random(3,8,1); $correctAnswer = Compute("2*$a^3*$sides*tan(pi/$sides)");	This is the problem set-up section of the problem. The solidsWW.swf applet will accept a piecewise defined function either in terms of x or in terms of y. We set $xy equal to x to define the function in terms of x. The two pieces of the function are defined in the variables $func1 and $func2, though any variable names beginning with the $ character will do. The applet also needs a maximum x-value for the profile graph. Usually you will want the $shapeType to be 'circle' but here we illustrate the 'poly' shapeType. Other types are accepted by the applet including: 'ellipse' and 'rectangle'. For 'ellipse' and 'rectangle' you will need to set the ratio of the side lengths. For 'poly' you will need to set the number of sides of the regular polygon. Here the number of sides is a random integer from 3 to 8.
######################################### # How to use the solidWW applet. # Purpose: The purpose of this applet # is to help with visualization of # solids # Use of applet: The applet state # consists of the following fields: # xmax - the maximum x-value. # ymax is 6/5ths of xmax. the minima # are both zero. # captiontxt - the initial text in # the info box in the applet # shapeType - circle, ellipse, # poly, rectangle # piece: consisting of func and cut # this is a function defined piecewise. # func is a string for the function # and cut is the right endpoint # of the interval over which it is # defined # there can be any number of pieces # ######################################### # What does the applet do? # The applet draws three graphs: # a solid in 3d that the student can # rotate with the mouse # the cross-section of the solid # (you'll probably want this to # be a circle # the radius of the solid which # varies with the height ######################################### ################################### # Create link to applet ################################### $appletName = "solidsWW"; $applet = FlashApplet( codebase => findAppletCodebase("$appletName.swf"), appletName => $appletName, appletId => $appletName, setStateAlias => 'setXML', getStateAlias => 'getXML', setConfigAlias => 'setConfig', maxInitializationAttempts => 10, height => '550', width => '595', bgcolor => '#e8e8e8', debugMode => 0, submitActionScript => '' ); ################################### # Configure applet ################################### $applet->configuration(qq{<xml><plot> <xy>$xy</xy> <captiontxt>'Compute the volume of the figure shown.' </captiontxt> <shape shapeType='$shapeType' sides='$sides' ratio='1.5'/> <xmax>$xmax</xmax> <theColor>0x0066cc</theColor> <profile> <piece func='$func1' cut='$a'/> <piece func='$func2' cut='$xmax'/> </profile> </plot></xml>}); $applet->initialState(qq{<xml><plot> <xy>$xy</xy> <captiontxt>'Compute the volume of the figure shown.' </captiontxt> <shape shapeType='$shapeType' sides='$sides' ratio='1.5'/> <xmax>$xmax</xmax> <theColor>0x0066cc</theColor> <profile> <piece func='$func1' cut='$a'/> <piece func='$func2' cut='$xmax'/> </profile> </plot></xml>}); TEXT( MODES(TeX=>'object code', HTML=>$applet->insertAll( debug=>0, includeAnswerBox=>0, )));	This is the Applet link section of the problem. Those portions of the code that begin the line with # are comments and can be omitted or replaced with comments appropriate to your particular problem. You must include the section that follows # Create link to applet. If you are embedding a different applet, from the solidsWW applet, put your applet name in place of 'solidsWW' in the line $appletName = "solidsWW";. Enter the height of the applet in the line height => '550', in place of 550 and the width in the line width => '595', in place of 595. The lines $applet->configuration(qq{<xml><plot> <xy>$xy</xy> <captiontxt>'Compute the volume of the figure shown.'</captiontxt> <shape shapeType='$shapeType' sides='3' ratio='1.5'/> <xmax>$xmax</xmax> <theColor>0x0066cc</theColor> <profile> <piece func='$func1' cut='$a'/> <piece func='$func2' cut='$xmax'/> </profile> </plot></xml>}); and $applet->initialState(qq{<xml><plot> <xy>$xy</xy> <captiontxt>'Compute the volume of the figure shown.'</captiontxt> <shape shapeType='$shapeType' sides='3' ratio='1.5'/> <xmax>$xmax</xmax> <theColor>0x0066cc</theColor> <profile> <piece func='$func1' cut='$a'/> <piece func='$func2' cut='$xmax'/> </profile> </plot></xml>}); configure the applet. The configuration of the applet is done in xml. The argument of the function is set to the value held in the variable $xy, the captiontxt that appears initially in the information box in the applet is set to Compute the volume of the figure shown., the shapeType is set to the variable $shapeType, $sides gives the number of sides of the regular polyogon, and ratio is ignored when the shapeType is set to 'poly', the color is set in hexadecimal with the xml code <theColor>0x0066cc</theColor> (this can be omitted and a default color will be used), the piecewise function is defined with the lines <piece func='$func1' cut='$a'/><piece func='$func2' cut='$xmax'/> where $func1 and $func2 define the function and cut specifies the right endpoint for which the given function definition applies. The function definition may have a single piece or more pieces in its definition. The code TEXT( MODES(TeX=>'object code', HTML=>$applet->insertAll( debug=>0, includeAnswerBox=>0, reinitialize_button=>$permissionLevel>=10, ))); actually embeds the applet in the WeBWorK problem. Answer submission and checking is done within WeBWorK. The applet is intended to aid with visualization and is not used to evaluate the student submission.
BEGIN_TEXT $BR $BR Find the volume of the figure shown. The cross-section of the figure is a regular $sides-sided polygon. The area of the polygon can be computed as a function of the length of a line segment from the center of the $sides-sided polygon to the midpoint of one of its sides and is given by \($sides x^2\tan\left(\frac{\pi}{$sides}\right)\) where \(x\) is the length of the bisector of one of the sides (shown in black on the cross-section graph). A formula similar to the cylindrical shells formula will then provide the volume of the figure. Simply replace \(\pi\) in the formula \[V=2\pi\int x f(x) dx\] with \($sides \tan\left(\frac{\pi}{$sides}\right)\) to find the volume of the solid shown where for this solid \[f(x)=\begin{cases}x&x\le $a\\ $b-x&$a<x\le $b\end{cases}\] for \(x=0\) to \($b\). \{ans_rule(35) \} $BR END_TEXT Context()->normalStrings;	This is the text section of the problem. The TEXT(beginproblem()); line displays a header for the problem, and the Context()->normalStrings; line sets how formulas are displayed in the text, and we reset this after the text section. Everything between the BEGIN_TEXT and END_TEXT lines (each of which must appear alone on a line) is shown to the student.
#################################### # # Answers # ## answer evaluators ANS( $correctAnswer->cmp() ); ENDDOCUMENT();	This is the answer section of the problem. The problem answer is set by the ANS( $correctAnswer->cmp() ); line. This is a standard WeBWorK answer checker. The ENDDOCUMENT(); command is the last command in the file.