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If you have a piece of tin 10 square what is the largest box with an open top?
Wiki User
∙ 14y ago
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.
Wiki User
∙ 14y ago
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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
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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
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