Question

The volume of a rectangular prism is 12x^5 -27x^3. What are the dimensions of the prism?

Answer 1

How do you get the volume of a rectangular prism?

To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.

`V=12x^5-27x^3`
`\begin{gathered} V=\text{lwh} \\ \text{where} \\ l=\text{length}\mathrm{}w=\text{width,h}=\text{height} \\ Volume=12x^5-27x^3 \end{gathered}`
`\begin{gathered} v=12x^5-27x^3 \\ =3x^3(4x^2-9) \\ =3x^3((2x)^2-3^2) \end{gathered}`

Assume the length is the

`\begin{gathered} length=3x^3 \\ (2x)^2-3^2 \\ \text{difference of two square} \\ (2x-3)(2x+3) \\ \text{width}=2x-3 \\ \text{height = 2x+3} \end{gathered}`

Therefore the dimension of the prism are

`\begin{gathered} l=3x^3 \\ w=2x-3 \\ h=2x+3 \end{gathered}`