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You really should consider trying this yourself before reading the answer, and you should understand the answer, otherwise you will not learn the lesson. Read each step, and do not proceed unless you understand it.
To maximize the volume of an open box made from a sheet of material 10 by 10, by cutting equal squares of side x from the corners and folding up the sides, first draw the box...
The box is 10-2x by 10-2x by x. Try again to draw it...
The volume of the box is (10-2x)(10-2x)x. Can you see the solution?
Simplify the volume. It is 4x3 - 40x2 + 100x. Can you see the solution?
Differentiate. This is a simple polynomial. Can you see the solution?
The deriviative is dy/dx = 12x2 - 80x + 100. Can you see the solution?
The maximum volume occurs when the deriviative is zero. Can you see the solution?
Solve for 12x2 - 80x + 100 = 0. How about the quadratic equation? Last chance to solve it yourself...
There are two roots of x: 5, and 5/3. 5, however, is not valid because you can not cut a square of 5 by 5 four times out of a square 10 by 10 and leave any volume at all, so the answer is 5/3.
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If 1200cmof material is avaiable to make a box with a square base and an open top find the largest possible volume of the box?
== ==1250347 because my calculus book tells me so
What are the square inches to a box?
To get the square inches in the box you need to multiply the length times width so a 2 inch by 4 inch box is 2x4= 8 square inches
How many box in a squre box?
4-8 boxes in a square box!
What is the correct name for square and squiggly brackets?
* round brackets, open brackets or parentheses: ( ) * square brackets, closed brackets or box brackets: [ ] * curly brackets, squiggly brackets, swirly brackets, braces, or chicken lips: { }
How can you calculate gram per square meter of corrugated box?
If you can destroy the box its easy. Cut a small piece from the board. Trim it to a regular shape such that you know the formula for its area : a rectangle is probably best. Measure the sides of the piece in metric units and convert these to metres (1 cm = 0.01 m, 1 mm = 0.001 m). Calculate the area in square metres. Measure the mass of the piece, and convert to grams, if necessary. Mass/Area = gsm. If you cannot damage the box, the area becomes much harder to measure. You need to measure all the sides, but also all the overlaps. Add all these area together. Divide the mass of the whole [empty] box by its total area.
