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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?

The volume of a rectangular prism is given by the formula Vlwh where I is the length of the prism w is the width and h is the height Which expression represents class=

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Answer:

The answer is [tex]6x^{3} +39x^{2}+54x[/tex]

Step-by-step explanation:

Volume of the rectangular prism = Length * Width * Height

Length (l) = [tex]x+2[/tex]

Width (w) = [tex]3x[/tex]

Height (h) = [tex]2x+9[/tex]

By substituting these values to the equation above,

Volume of the rectangular prism = [tex](x+2)*3x*(2x+9)[/tex]

                                                      =[tex](3x^{2} +6x)*(2x+9)[/tex]

                                                      =[tex]6x^{3} +27x^{2} +12x^{2} +54x[/tex]

                                                      =[tex]6x^{3} +39x^{2}+54x[/tex]

Therefore,

The answer is [tex]6x^{3} +39x^{2}+54x[/tex]

Answer:

Volume = [tex]6x^3+39x^2+54x[/tex]

Step-by-step 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 [tex]lwh[/tex] .

We will also use formula: [tex]a(b+c)=ab+ac[/tex]

Here,

[tex]l=x+2\\w=3x\\h=2x+9[/tex]

Therefore,

volume of rectangular prism is calculated as follows:

[tex]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[/tex]

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