Question

Andre wants to make an open box by cutting out corners of a 22 inch by 28 inch poster board and then folding up the sides. The volume V(x) in cubic inches of the open top box is a function of the side length x in inches of the square cutouts. Write and expression for v(x)

Answer 1

Answer:

v(x) = x(22 - 2x)(28 - 2x)

Step-by-step explanation:

The length of the box = 28 - 2x inches,

The width = 22 - 2x inches and the height  = x inches.

v(x) = x * width * length.

Answer 2

The volume of the open top box is $V(x) = (28 - 2x)(22 - 2x)(x)$ cubic inches

The volume of the box is V = (length)(width)(height).

Let the cutout side length be $x$ inch,

We are to cut out $x$ by

So, the length of the box is $28 - 2x$ inch

the width of the box is $22 - 2x$ inch and

the height of the box is $x$ inch

Now, substituting the values in the volume formula, we get

$V(x) = (28 - 2x)(22 - 2x)(x)$ cubic inches

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