Question

A rectangular prism has dimensions of x + 1, x - 1, and x. Write an expression for the total volume of the prism.

Answer 1

We have been given the dimensions of the rectangular prism.

Lets say that the length, width, and height of the rectangular prism are:

Length
`= x+1`

Width
`=x-1`

Height
`=x`

Volume of a rectangular prism is given by:

`length * width* height`

Plugging the values of length, width, and height, we get:

Total volume of the prism
`= (x+1)*(x-1)* x`

`=(x^2-1)x=x^3-x` (we have used
`(a+b)* (a-b)=a^2-b^2`)

So, the expression for the total volume of the prism is:

`(x^3-x)`