document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1161726>Question 1161726</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A component (circle-shaped with a diameter measuring 60 cm) is stamped out of sheet steel. A square(with side measuring 30 cm) in the center of that circle is discarded. These components are stamped out of a continuous steel coil with a width of 70 cm. The stamping process requires a gap of 25mm between each component. The steel coil is supplied in lengths of 25 meters costing $200.\r<BR>\n" );
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document.write( "a) What is the approximate percentage of steel wasted including the center square?<BR>\n" );
document.write( "b) Assuming minimal wastage, how many components can be produced from each 25-meter coil?<BR>\n" );
document.write( "c) What is the approximate cost of a component if the scrap is sold at 50% of the cost?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #785338 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=785338\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> b) You can stamp up to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2840%29 ALIGN=MIDDLE  ALT=\"highlight%2840%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > circles,<BR>\n" );
document.write( "Stamping the 60cm diameter circles centered on the mid-width of the sheet, 25mm (2.5cm) apart from each other would allow us to stamp along the 25m (2500cm) steel coil<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2500cm%2F%2860cm%2B2.5cm%29=40 ALIGN=MIDDLE  ALT=\"2500cm%2F%2860cm%2B2.5cm%29=40\"   DISABLED_style= \"max-width:90%; height:auto;\" >circles.<BR>\n" );
document.write( "In fact <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40 ALIGN=MIDDLE  ALT=\"40\"   DISABLED_style= \"max-width:90%; height:auto;\" > circles with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40-1=39 ALIGN=MIDDLE  ALT=\"40-1=39\"   DISABLED_style= \"max-width:90%; height:auto;\" > gaps between them, adding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.5cm ALIGN=MIDDLE  ALT=\"2.5cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > per gaps adds to a length of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2A%2860cm%29%2B39%2A%282.5cm%29=2497.5cm ALIGN=MIDDLE  ALT=\"40%2A%2860cm%29%2B39%2A%282.5cm%29=2497.5cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and we could use the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2500cm-2497.5cm=2.5cm ALIGN=MIDDLE  ALT=\"2500cm-2497.5cm=2.5cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > leftover length<BR>\n" );
document.write( "to leave some space between the circles at the ends and the beginning and end of the coil.<BR>\n" );
document.write( "Offsetting the circles so they are shifted a bit to the left and the right, makes the string of circles a little shorter, but not short enough to fit an additional circle.<BR>\n" );
document.write( "The most you could offset centers is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70cm-60cm=10cm ALIGN=MIDDLE  ALT=\"70cm-60cm=10cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and making the distance between the centers centers <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB=62.5cm ALIGN=MIDDLE  ALT=\"AB=62.5cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > , would make the circles look like this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28650%2C400%2C-5%2C125%2C-40%2C40%2C%0D%0Ared%28rectangle%280%2C-35%2C121.7%2C35%29%29%2Crectangle%28121.7%2C-35%2C150%2C35%29%2C%0D%0Ared%28circle%2830%2C-5%2C30%29%29%2Cred%28circle%2830%2C-5%2C0.4%29%29%2Cred%28circle%2830%2C-5%2C0.2%29%29%2C%0D%0Ared%28circle%2891.7%2C5%2C30%29%29%2Cred%28circle%2891.7%2C5%2C0.4%29%29%2Cred%28circle%2891.7%2C5%2C0.2%29%29%2C%0D%0Atriangle%2830%2C-5%2C91.7%2C-5%2C91.7%2C5%29%2Crectangle%2891.8%2C-5%2C90.7%2C-4%29%2C%0D%0Alocate%2828.5%2C-5.5%2CA%29%2Clocate%2891%2C8.5%2CB%29%2Clocate%2891%2C-5.1%2CC%29%2C%0D%0Ared%28circle%28151.7%2C-5%2C30%29%29%2Carrow%280%2C-5%2C30%2C-5%29%2Carrow%2830%2C-5%2C0%2C-5%29%2C%0D%0Aarrow%2891.7%2C5%2C121.7%2C5%29%2Carrow%28121.7%2C5%2C91.7%2C5%29%2Carrow%28100%2C0%2C100%2C-35%29%2C%0D%0Aarrow%28100%2C0%2C100%2C35%29%2Clocate%2813%2C-5%2C30cm%29%2Clocate%28104.7%2C5%2C30cm%29%2C%0D%0Alocate%28101%2C0%2C70cm%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC=10cm ALIGN=MIDDLE  ALT=\"BC=10cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC=sqrt%2862.5%5E2%2B10%5E2%29 ALIGN=MIDDLE  ALT=\"AC=sqrt%2862.5%5E2%2B10%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm=61.7cm ALIGN=MIDDLE  ALT=\"cm=61.7cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Each pattern with 2 circles (red rectangle) takes up<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30cm%2B61.7cm%2B30cm=121.7cm ALIGN=MIDDLE  ALT=\"30cm%2B61.7cm%2B30cm=121.7cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > , so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40 ALIGN=MIDDLE  ALT=\"40\"   DISABLED_style= \"max-width:90%; height:auto;\" > circles require <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2B121.7=2434cm ALIGN=MIDDLE  ALT=\"40%2B121.7=2434cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > out of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2500cm ALIGN=MIDDLE  ALT=\"2500cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > length of the coil.<BR>\n" );
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document.write( "a) The area of each circle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Aradius%5E2=pi%2A%2830cm%29%5E2=900pi ALIGN=MIDDLE  ALT=\"pi%2Aradius%5E2=pi%2A%2830cm%29%5E2=900pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm%5E2 ALIGN=MIDDLE  ALT=\"cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The area of the square cut off is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2830cm%29%2A%2830cm%29=900cm%5E2 ALIGN=MIDDLE  ALT=\"%2830cm%29%2A%2830cm%29=900cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The area of each component stamped is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28900pi-900%29 ALIGN=MIDDLE  ALT=\"%28900pi-900%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm%5E2=900%28pi-1%29 ALIGN=MIDDLE  ALT=\"cm%5E2=900%28pi-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm%5E2=approx. ALIGN=MIDDLE  ALT=\"cm%5E2=approx.\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=900%283.1416-1%29=900%2A2.1416cm%5E2=1927.44cm%5E2 ALIGN=MIDDLE  ALT=\"900%283.1416-1%29=900%2A2.1416cm%5E2=1927.44cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The total area of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40 ALIGN=MIDDLE  ALT=\"40\"   DISABLED_style= \"max-width:90%; height:auto;\" > stamped components is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2A1927.44cm%5E2=77097.6cm%5E2 ALIGN=MIDDLE  ALT=\"40%2A1927.44cm%5E2=77097.6cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The area of a sheet coil <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=70cm ALIGN=MIDDLE  ALT=\"70cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > wide and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2500cm ALIGN=MIDDLE  ALT=\"2500cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > long is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2870cm%29%2A%282500cm%29=175000cm%5E2 ALIGN=MIDDLE  ALT=\"%2870cm%29%2A%282500cm%29=175000cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Out of that surface area <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=77097.6cm%5E2 ALIGN=MIDDLE  ALT=\"77097.6cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > turns into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40 ALIGN=MIDDLE  ALT=\"40\"   DISABLED_style= \"max-width:90%; height:auto;\" > components, and the rest is \"steel wasted including the center square\".<BR>\n" );
document.write( "The surface area of the steel wasted including the center square\" is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=175000cm%5E2-77097.6cm%5E2=97902.4cm%5E2 ALIGN=MIDDLE  ALT=\"175000cm%5E2-77097.6cm%5E2=97902.4cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "As a percentage of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=175000cm%5E2 ALIGN=MIDDLE  ALT=\"175000cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the coil, that is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2897902.4%2F175000cm%5E2%29%2A%22100%25%22=%22approx.%22 ALIGN=MIDDLE  ALT=\"%2897902.4%2F175000cm%5E2%29%2A%22100%25%22=%22approx.%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%2255.9%25%22%29=%22approx.%22 ALIGN=MIDDLE  ALT=\"highlight%28%2255.9%25%22%29=%22approx.%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%2256%25%22%29 ALIGN=MIDDLE  ALT=\"highlight%28%2256%25%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "c) The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2256%25%22=56%2F100=0.56 ALIGN=MIDDLE  ALT=\"%2256%25%22=56%2F100=0.56\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the coil wasted represents a cost of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.56%2A%22%24200%22=%22%24112%22 ALIGN=MIDDLE  ALT=\"0.56%2A%22%24200%22=%22%24112%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Selling it at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2250%25%22=50%2F100=0.5 ALIGN=MIDDLE  ALT=\"%2250%25%22=50%2F100=0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the cost reclaims <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.5%2A%22%24112%22=%22%2456%22 ALIGN=MIDDLE  ALT=\"0.5%2A%22%24112%22=%22%2456%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "making the cost of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40 ALIGN=MIDDLE  ALT=\"40\"   DISABLED_style= \"max-width:90%; height:auto;\" > components <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%24200%22-%22%2456%22-%22%24144%22 ALIGN=MIDDLE  ALT=\"%22%24200%22-%22%2456%22-%22%24144%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and the cost per component<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22%24144%22%2F40=highlight%28%22%243.60%22%29 ALIGN=MIDDLE  ALT=\"%22%24144%22%2F40=highlight%28%22%243.60%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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