an open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at?
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While Albert has found the correct solution using calculus, the question asked how to find the solution with graphing.  So, if you don't care how you find the answer, use Albert's.  But if you need to graph it to find the solution, you use the function that Albert got V(x)=x(6-2x)(8-2x) and graph the resulting cubic function (explained well by Just Wondering).  You will see a graph that increases from -infinity up to about 24 (on the V), then decreases to about -3.5, and then increases to infinity.  You want to find the x value and V value at that first "hump," or maximum.  If you are using a graphing calculator you can use the "Maximum" function to see that Albert's answer is approximately correct.
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It implies that the box is 10 square so each dimension is 10.  Volume of a cube = h x d x w , or in this case 10 x 10 x 10 = 1000
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1) Rearrange so\ny = -(5/3)x + (2/3)\nThis means the perpendicular to this line (which the point must lie on) is of the form\ny = (3/5)x + n \nlet (a,b) = the point we require, so\nb = -(5/3)a + (2/3)   equation 1\nand -5 = -4(3/5) + n so n = -(13/5)   equation 2\nand b = a(3/5) + n  equation 3\nsubstitution of equations 1 and 2 into 3 give:\n-(5/3)a + (2/3) = a(3/5) - 13/5\nso a = 49/34\nand consequently b = -59/34\nso the point is (49/34, -59/34)\n\n2) let h = height of box and l = width of box = length of box (square base)\nso volume, v = hl^2\nand material area, a =l^2 + 4lh = 1300 cm^2\nso h = (1300-l^2)/(4l)\nso now v = (1300l - l^3)/4\nfor max volume \ndv/dl = 0 \nso dv/dl = (1300 - 3l^2)/4\n(1300 - 3l^2)/4 = 0 when l = sqrt(1300/3)\nwe take only the positive solution as the negative is meaningless in this problem.\nto check this is indeed a maximum value (as oppose to a minimum) we derive d^v/dl^2:\nd^v/dl^2 = -3l/2 so for l = sqrt(1300/3) this is always negative confirming this is a maxima.\nso now, v  = (1300l - l^3)/4\nsubstitute l = 20.817 cm\ngives volume, v = 4510.28 cm^3
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Top line little square box with green inverted arrows in it
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Form a triagle. Cut the "corners" off.
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in an envelope with a piece of cardboard protecting both sides. so that it is sandwiched.
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Lots of fields are rectangular.  The baseball infield is a square.
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6 faces, 12 edges, 8 vertices
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You want the VOLUME of the rectangular solid.\n(A "cube" is a solid with equal height, width, and depth - like a die.)\n\nThe volume = 15.5 * 10.5 * 9.375 = 1525.78125 cubic inches
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im assumuing you mean a rectangle? If it was a square itd be 400, if its a rectangle its 80l-l^2
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Square and Rectangle= lenght*height\ntriangle=base*height divided by 2
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here is a cut out model\n\nits quite a way down the page, you need a shoe box.
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4x10 , 8x5 it amounts to 4ft x10ft
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when you cut out the plywood and make them alittle taller you can also make a box for people to stand on behind the picture so they won't trip i've seen this done at the fair's hope this helps
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You can't just draw one? It's 10 boxes across the top and down the side, starting with 0 and going to 9 (and no, the corner doesn't share both sides). All you need are a pen and a ruler.
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Yes form a hexagon with 6 of the boards and then place the other six boards so they meet at the center. Each pig will then have an equilateral triangle as a pen.
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I like  this question because answering it I found  out this totally cool thing. The table top game of "Go" board is not square!\n\nIt is usually a rectangle about 15 x 14 in proportion. Almost square, but 7 percent longer on one side.\n\nSome boards are a 19 x 19 grid, others are 17 x 17, 13 x 13 or even 9 x 9 for shorter games!\n\nThe boards were traditionally made out of a thick block of wood, with a hollow pyramid carved into the underside for strength and to make it sound better when the pieces (black and white stones) are placed.\n\nIt is also cool to find out that the black stones (kinda shaped like M&M candies) are bigger than the white ones. Thanks for asking a question which taught me more about a cool game.