Answer:
The required function that gives the volume V in terms of x is [tex]V=\dfrac{x^3}{3}-\dfrac{4x^2}{3}[/tex].
Step-by-step explanation:
Consider the provided information.
The height of the pyramid to be 4 inches less than the length of a side of the base.
Let the length of a side of the base is = x
Thus, the height of the pyramid = x-4
The volume of the sculpture is 200 cubic inches
Volume of a pyramid is: [tex]V=\dfrac{1}{3} \text{Area of Base}\times\text{Height}[/tex]
The base of pyramid is square.
So, the area of base = [tex]x^2[/tex]
Substitute the respective values in the above formula.
[tex]V=\dfrac{1}{3}\times(x^2)\times(x-4)[/tex]
[tex]V=\dfrac{1}{3}\times(x^3-4x^2)[/tex]
[tex]V=\dfrac{x^3}{3}-\dfrac{4x^2}{3}[/tex]
Hence, the required function that gives the volume V in terms of x is [tex]V=\dfrac{x^3}{3}-\dfrac{4x^2}{3}[/tex].
