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

Answer:

The required function that gives the volume V in terms of x is $V=\dfrac{x^3}{3}-\dfrac{4x^2}{3}$.

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: $V=\dfrac{1}{3} \text{Area of Base}\times\text{Height}$

The base of pyramid is square.

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

Substitute the respective values in the above formula.

$V=\dfrac{1}{3}\times(x^2)\times(x-4)$

$V=\dfrac{1}{3}\times(x^3-4x^2)$

$V=\dfrac{x^3}{3}-\dfrac{4x^2}{3}$

Hence, the required function that gives the volume V in terms of x is $V=\dfrac{x^3}{3}-\dfrac{4x^2}{3}$.