Question

The volume of a rectangular prism is (x^3 – 3x^2 + 5x – 3), and the area of its base is (x^2 – 2). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism?

Answer 1

The height of the prism is equal to
`h=(x^(3)-3x^(2)+5x-3)/(x^(2)-2)`

Explanation:

we know that

The volume of a rectangular prism is equal to

`V=Bh`

where

B is the area of the base of the prism

h is the height of the prism

In this problem we have

`V=x^(3)-3x^(2)+5x-3`

`B=x^(2)-2`

substitute in the formula and solve for h

`x^(3)-3x^(2)+5x-3=(x^(2)-2)h`

`h=(x^(3)-3x^(2)+5x-3)/(x^(2)-2)`