Question

You are making a sculpture that is a pyramid with a square base. You want the height of the pyramid to be 4 inches less than the length of a side of the base. You want the volume of the sculpture to be 200 cubic inches. Write a function that gives the volume V of the sculpture in terms of x.

Answer 1

The required function that gives the volume V in terms of x is
`V=(x^3)/(3)-(4x^2)/(3)`.

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:
`V=(1)/(3) \text{Area of Base}*\text{Height}`

The base of pyramid is square.

So, the area of base =
`x^2`

Substitute the respective values in the above formula.

`V=(1)/(3)*(x^2)*(x-4)`

`V=(1)/(3)*(x^3-4x^2)`

`V=(x^3)/(3)-(4x^2)/(3)`

Hence, the required function that gives the volume V in terms of x is
`V=(x^3)/(3)-(4x^2)/(3)`.