document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=116714>Question 116714</A>: <I><SPAN STYLE=\"word-break: break-all;\">  hi please help me with this. this is only what i am not done with an have to hand this in tomorrow. it is already 10 at night here. I am really worried<BR>\n" );
document.write( "please help me \r<BR>\n" );
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document.write( "Kayla has 1.5 m (squared) of sheet metal to build a storage box for firewood. <BR>\n" );
document.write( "a) what is the surface area of the metal , in square centimeters? \r<BR>\n" );
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document.write( "b) What are the dimensions for this square based prism box with maximum volume including a lid ?\r<BR>\n" );
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document.write( "c)If the box doesnt have a lid, what are the dimensions of the square based prism. Round off to the nearest tenth of a centimeters.hint( make a table of possible boxes) \r<BR>\n" );
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document.write( "any help will be apreciated \r<BR>\n" );
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document.write( "for a) i think the area is 150 cm squared \r<BR>\n" );
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document.write( "for B according to my calculations the dimensions are 5 x 5 x 5 cm and the volume is 125 cm (cubed) \r<BR>\n" );
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document.write( "I dont know if my answers are correct and I am stuck on c) \r<BR>\n" );
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document.write( "any help will be greatly appreciated . Please help me <BR>\n" );
document.write( "I need help desperately \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 #84893 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=84893\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Desperate times call for desperate action. Here's some help. You may need to re-post this <BR>\n" );
document.write( "problem to see if another tutor can supply some more info.<BR>\n" );
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document.write( "First part. The way I interpret what you wrote is that Kayla has 1.5 square meters of material.<BR>\n" );
document.write( "[Note that this is NOT the same as a 1.5 meter square which is 1.5 meters on a side for<BR>\n" );
document.write( "an area of 1.5^2 = 2.25 square meters.]<BR>\n" );
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document.write( "There are 10,000 square centimeters in each square meter ... think that 1 square meter could<BR>\n" );
document.write( "be a metal sheet 1 meter on a side. But 1 meter is 100 cm. So a sheet of metal that is <BR>\n" );
document.write( "1 meter on a side is equal to a sheet of metal that is 100 cm on a side. So a 1 meter by 1 meter<BR>\n" );
document.write( "sheet of metal is equivalent to a 100 cm by 100 cm piece of material. A 100 by 100 cm sheet <BR>\n" );
document.write( "is 10,000 square cm. So the conversion from square meters to square cm is 10,000 times sq meters <BR>\n" );
document.write( "equals sq cm. <BR>\n" );
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document.write( "And since Kayla has 1.5 square meters of metal, 10,000 times that means that the metal Kayla <BR>\n" );
document.write( "has is 15,000 square centimeters of metal. <BR>\n" );
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document.write( "Second part. I have just about convinced myself that a cube is the type of box that will <BR>\n" );
document.write( "contain the maximum volume. And a cube has 6 sides (Top, Bottom, 4 Sides around). Since<BR>\n" );
document.write( "a cube has equal length sides on all edges, the area of each side is S^2 and there are,<BR>\n" );
document.write( "as stated, 6 sides. So the total area of material needed to make a cube is 6S^2 and this<BR>\n" );
document.write( "area must come from 15,000 sq cm of metal. Solve for S by using the equation<BR>\n" );
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document.write( "6S^2 = 15000<BR>\n" );
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document.write( "Divide both sides by 6 and you have:<BR>\n" );
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document.write( "S^2 = 2500 <BR>\n" );
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document.write( "Take the square root of both sides and you have:<BR>\n" );
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document.write( "S = sqrt(2500) = 50 cm<BR>\n" );
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document.write( "The box with the maximum volume that can be built from 1.5 square meters of material and<BR>\n" );
document.write( "having a lid is (I think) a cube having each side 50 cm long. Not a very big box for firewood. <BR>\n" );
document.write( "(That's a cube that is only about 19.6 inches by 19.6 inches by 19.6 inches.)<BR>\n" );
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document.write( "Part c.<BR>\n" );
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document.write( "If Kayla is going to build a box with no lid and a square bottom, the amount of material needed<BR>\n" );
document.write( "for the bottom of the box will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5E2 ALIGN=MIDDLE  ALT=\"S%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > where S is a side of the bottom of the box. The <BR>\n" );
document.write( "question is, how tall can the box be? The material left after making the bottom of the box<BR>\n" );
document.write( "is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15000 ALIGN=MIDDLE  ALT=\"15000\"   DISABLED_style= \"max-width:90%; height:auto;\" > sq cm minus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5E2 ALIGN=MIDDLE  ALT=\"S%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm. Each of the four sides that need to be build will be H, the height<BR>\n" );
document.write( "of the box, times S in area. And since there are four sides, the total area of material needed<BR>\n" );
document.write( "for the sides is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2AS%2AH ALIGN=MIDDLE  ALT=\"4%2AS%2AH\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Since the amount of metal left after making the bottom of the box<BR>\n" );
document.write( "is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15000+-+S%5E2 ALIGN=MIDDLE  ALT=\"15000+-+S%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this is the amount of material left to build the sides which requires a total<BR>\n" );
document.write( "of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2AS%2AH ALIGN=MIDDLE  ALT=\"4%2AS%2AH\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Set these two amounts equal and solve for H:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2AS%2AH+=+15000+-+S%5E2 ALIGN=MIDDLE  ALT=\"4%2AS%2AH+=+15000+-+S%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide both sides by 4*S and you have:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H+=+%2815000+-+S%5E2%29%2F%284%2AS%29 ALIGN=MIDDLE  ALT=\"H+=+%2815000+-+S%5E2%29%2F%284%2AS%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "And we know the volume of this box is the product of its dimensions or:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+H+%2A+S+%2A+S ALIGN=MIDDLE  ALT=\"V+=+H+%2A+S+%2A+S\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%2AS%5E2 ALIGN=MIDDLE  ALT=\"H%2AS%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute (15000 - S^2)/(4*S) for H in the volume equation to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+%2815000+-+S%5E2%29%2F%284%2AS%29%2AS%5E2 ALIGN=MIDDLE  ALT=\"V+=+%2815000+-+S%5E2%29%2F%284%2AS%29%2AS%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Cancel one of S in the numerator with the S in the denominator and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+%2815000+-+S%5E2%29%2AS%2F4 ALIGN=MIDDLE  ALT=\"V+=+%2815000+-+S%5E2%29%2AS%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now build yourself a table by assuming values for S and calculating the corresponding <BR>\n" );
document.write( "values for the Volume. <BR>\n" );
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document.write( "If I haven't made a mistake, here's a table of some values:<BR>\n" );
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document.write( "When S (the dimension of the square bottom) = ......... then Volume =<BR>\n" );
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document.write( "60 cm ................................................. 171,000 cm^3<BR>\n" );
document.write( "65 cm ................................................. 175,094 cm^3<BR>\n" );
document.write( "69 cm ................................................. 176,623 cm^3<BR>\n" );
document.write( "70 cm ................................................. 176,150 cm^3<BR>\n" );
document.write( "71 cm ................................................. 176,772 cm^3<BR>\n" );
document.write( "72 cm ................................................. 176,688 cm^3<BR>\n" );
document.write( "75 cm ................................................. 175,781 cm^3<BR>\n" );
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document.write( "It looks as if the volume maximizes around the value S = 71 cm<BR>\n" );
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document.write( "And when S = 71 cm the height is given by:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H+=+%2815000+-+S%5E2%29%2F%284%2AS%29=+%281500-+71%5E2%29%2F%284%2A71%29+=+35.0669+cm ALIGN=MIDDLE  ALT=\"H+=+%2815000+-+S%5E2%29%2F%284%2AS%29=+%281500-+71%5E2%29%2F%284%2A71%29+=+35.0669+cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So the dimensions of the box that appear to maximize the volume are around<BR>\n" );
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document.write( "71 cm by 71 cm by 35.0669 cm where the 71 by 71 is the bottom and the 35 is the height.<BR>\n" );
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document.write( "I've done this so fast I haven't had time to check it, but maybe it will help you to understand<BR>\n" );
document.write( "the problem a little better and get some credit tomorrow. Check my work.<BR>\n" );
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document.write( "Hope I'm not too late. </SPAN>\n" );
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