SOLUTION: An open-top box is to be constructed from a 4 foot by 6 foot rectangular cardboard by cutting out equal squares at each corner and folding up the flaps. Let x denote the length of
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Question 77542: An open-top box is to be constructed from a 4 foot by 6 foot rectangular cardboard by cutting out equal squares at each corner and folding up the flaps. Let x denote the length of each side of the square to be cut out.
a) Find the function V that represents the volume of the box in terms of x.
b) Graph this function and show the graph over the valid range of the variable x..
c) Using the graph, what is the value of x that will produce the maximum volume?
You can put this solution on YOUR website! An open-top box is to be constructed from a 4 foot by 6 foot rectangular cardboard by cutting out equal squares at each corner and folding up the flaps. Let x denote the length of each side of the square to be cut out.
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The dimensions of the box will be (4-2x) by (6-2x) by x
:
a) Find the function V that represents the volume of the box in terms of x.
V = (4-2x)*(6-2x)*x
V = 4x^3 - 20x^2 + 24x
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b) Graph this function and show the graph over the valid range of the variable x..
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c) Using the graph, what is the value of x that will produce the maximum volume?
It is about .8 ft or about 9.6 inches.
Max vol would be 2.4 * 4.4 * .8 = 8.45 cu ft
