Question

Lucy cuts 4 squares with side length x in. from the corners of a 12 in. by 18 in. cardboard rectangle. She folds the remaining cardboard to make a tray that is x in. high. Write and simplify a polynomial function for the volume V of the tray in terms of x.
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Answer 1

Answer:

Volume of tray =$4x^{3} -60x^{2} +216x$

Step-by-step explanation:

The Dimensions of rectangular cardboard is given by 12 inches by 18 inches

Length of the rectangular cardboard = 18 inches

Width of the rectangular cardboard = 12 inches

if the square of sides x inches is cut from each corner of the rectangular cardboard and folded to make a tray, then we have

Length of the tray = length of cardboard - 2 (side of the square )

                               = $18-2x$

Width of the tray = width of cardboard - 2( side of square)

                            = $12-2x$

height of tray = sides of square

                       = x

volume of tray = Length × width × height

Volume of tray = $x(18-2x)(12-2x)$

first we multiply (12-2x) and (18-2x)

Volume of tray =$x(18(12-2x)-2x(12-2x))$

                         =$x(216-36x-24x+4x^{2})$

                         =$x(4x^{2}-60x+ 216)$

                         =$4x^{3} -60x^{2} +216x$

Hence the volume of tray =$4x^{3} -60x^{2} +216x$

Answer 2

The volume of the Tray is given by the equation $4x^3-60x^2+216x$ and this can be determined by using the given data.

Given :

• Lucy cuts 4 squares with side length x in. from the corners of a 12 in. by 18 in. cardboard rectangle.
• She folds the remaining cardboard to make a tray that is x in.

If the square is cut from each corner of the cardboard and folded to make a tray, then according to the given data:

Tray length = 18 - 2x

Tray width = 12 - 2x

Tray height = x

Now, the volume of the tray is given by the expression:

The volume of Tray = $x(12-2x)(18-2x)$

Simplify, the above expression.

$\rm Volume = (12x - 2x^2)(18-2x)$

$\rm Volume = 216x -24x^2-36x^2+4x^3$

$\rm Volume = 4x^3-60x^2+216x$

For more information, refer to the link given below:

https://brainly.com/question/19501533