Question

Find the volume of a rectangular prism if the length is 4x, the width is 5x, and the height is x2 + x + 2. Use the formula V = l ⋅ w ⋅ h, where l is length, w is width, and h is height, to find the volume

Answer 1

(4x)(5x)(x^2+x+2)

20x^2(x^2+x+2)

Answer: 20x^4+20x^3+40x^2 cubic units

Answer 2

`20x^4+20x^3+40x^2` cubic units

Explanation:

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

As per the statement:

Given the length(l) = 4x units , width(w) = 5x units, and height(h) =
`x^2+x+2` units

We have to find the volume of a rectangular prism.

Use the formula:

`V = lwh`

Substitute the given values we have;

`V = 4x \cdot 5x \cdot (x^2+x+2)`

⇒
`V =20x^2 \cdot (x^2+x+2)`

Using distributive property:
`a \cdot (b+c) = a\cdot b+ a\cdot c`

`V = 20x^4+20x^3+40x^2`

Therefore, the volume of rectangular prism is,
`20x^4+20x^3+40x^2` cubic units