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

Answer:

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

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 $lwh$ .

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

Answer:

The answer is $6x^{3} +39x^{2}+54x$

Step-by-step 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 $6x^{3} +39x^{2}+54x$