(a).

Let the volume of the pyramid is .

Where is area of the base.

Where is height of the praymid.

Let  represent length of one of the sides of square base.

The area of the sqquare base of the pyramid is .

The height of the pyramid is .

Substiute the values of ,, in the volume of the parymid, .

The volume function of the model in terms of its length is .

(b).

Let volume of the model is .

Subustiute the value in .

If the volume of the model is cubic inches then the equation is .

(c).

Consider .

.

.

The above polynomial has sign variation. so , it has positive real zero.

Graph :

Draw the coordinate plane.

Graph the function .

Observe the graph:

The function touches the  axis at . 

Synthetic Division:

The function is .

Replace zero in the missing term .

Perform the synthetic division method by testing .

must be a positive value because, the above polynomial has sign variation. so , it has posotive real zero.

Also only has positive real zero.

Therefore the base is  inches by inches and also the height of the model is  inches.

(a).

The volume function of the model in terms of its length is .

(b).

If the volume of the model is cubic inches then the equation is .

(c).

Base is inches by inches

Height is inches.