(a).

Let the length of the block,

            width of the block,

            height of the block.

And be the equal amount of clay removed from the block.

Now length of the block,

        width of the block,

        height of the block.

Volume of the block, .

 .

The polynomial function is  .

(b).

Length of the box must be or .

Height of the box must be or .

Width of the box must be or .

Therefore, the domain is .

Subustiute the values of in the obtained polynomial equation  to get the values of . 

Graph : 

(1)  Draw the coordinate planes.

(2)  Plot the points

(3) Connect the points with the smooth curve.

(c).

The original volume of the block is .

Amount of volume reduced by esteban is of the original volume.

Now the volume of the new block is .

Now the equation can be written as

.

(d).

Consider .

Let and .

Draw a coordinate plane.

Graph the functions and in the same axis.

Graph :

Observe the graph :

The two functions are intersects at .

Therefore, esteban should take about ft from each dimension.

(a).

The polynomial function is  .

(b).

Graph : 

(c).

.

(d).

Esteban should take about ft from each dimension.