Question

Using V = lwh, What is an expression for the volume of the following prism?

Answer 1

Given:

Length of the rectangular prism =
`(d-2)/(3d-9)`

Width of the rectangular prism =
`(4)/(d-4)`

Height of the rectangular prism =
`(2d-6)/(2d-4)`

To find:

The volume of the rectangular prism.

Solution:

We know that the volume of rectangular prism is:

`V=l* w* h`

Where, l is the length, w is the width and h is the height.

After substituting the given values, we get

`V=(d-2)/(3d-9)* (4)/(d-4)* (2d-6)/(2d-4)`

`V=(d-2)/(3(d-3))* (4)/(d-4)* (2(d-3))/(2(d-2))`

`V=((d-2)* 4* 2(d-3))/(3(d-3)* (d-4)* 2(d-2))`

Cancel out the common factors.

`V=(4)/(3* (d-4))`

`V=(4)/(3(d-4))`

`V=(4)/(3d-12)`

Therefore, the correct option is C.