Question

The volume of a rectangular prism is given by the formula V=lwh, where I is the length of the prism, w is the width, and h is the height. Which expression represents the volume of the following rectangular prism?

Answer 1

Volume =
`6x^3+39x^2+54x`

Explanation:

Prism is an object which has two bases which are parallel to each other and other faces are parallelograms .

Rectangular prism is a three dimensional figure which has 6 faces which are all rectangles .

Let l be the length of rectangular prism , w be the width of prism and h be the height of prism .

Then volume of rectangular prism is equal to
`lwh` .

We will also use formula:
`a(b+c)=ab+ac`

Here,

`l=x+2\\w=3x\\h=2x+9`

Therefore,

volume of rectangular prism is calculated as follows:

`V=\left ( x+2 \right )\left ( 3x \right )\left ( 2x+9 \right )\\=\left ( 3x^2+6x \right )\left ( 2x+9 \right )\\=3x^2\left ( 2x+9 \right )+6x\left ( 2x+9 \right )\\=6x^3+27x^2+12x^2+54x\\=6x^3+39x^2+54x`

Answer 2

The answer is
`6x^(3) +39x^(2)+54x`

Explanation:

Volume of the rectangular prism = Length * Width * Height

Length (l) =
`x+2`

Width (w) =
`3x`

Height (h) =
`2x+9`

By substituting these values to the equation above,

Volume of the rectangular prism =
`(x+2)*3x*(2x+9)`

=
`(3x^(2) +6x)*(2x+9)`

=
`6x^(3) +27x^(2) +12x^(2) +54x`

=
`6x^(3) +39x^(2)+54x`

Therefore,

The answer is
`6x^(3) +39x^(2)+54x`