An open box is to be made from a flat piece of material 8 inches long and 2 inches wide by cutting equal squares of length x from the corners and folding up the sides.
Write the volume V of the box as a function of x. Leave it as a product of factors, do not multiply out the factors.
V=?
length = 8-2x
width = 2-2x
height = x
volume = x(8-2x)(2-2x)
L=8-2x
W=2-2x
volumeV=LWh= (8-2x)(2-2x)(x)
To find the volume V of the box, we need to determine the dimensions of the box after cutting equal squares of length x from the corners and folding up the sides.
Let's start by drawing a diagram to visualize the box. We have a flat piece of material that is 8 inches long and 2 inches wide. We will cut equal squares from each corner and fold up the sides to form a box.
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Let's assume that we cut squares of length x from each corner. When we fold up the sides, the length of the box will be reduced by 2x (x from each end), and the width will be reduced by 2x (x from each side).
Thus, the dimensions of the box will be (8 - 2x) inches by (2 - 2x) inches by x inches.
Therefore, the volume V of the box is given by:
V = (8 - 2x)(2 - 2x)(x)
To leave the volume in factored form, we do not multiply out the factors. So the final expression for the volume of the box as a function of x is:
V = (8 - 2x)(2 - 2x)(x)