Question

Find the volume of a rectangular prism if the length is 4x, the width is 2x, and the height is x3 + 3x + 6. Use the formula

V = l ⋅ w ⋅ h, where l is length, w is width, and h is height, to find the volume.

6x5 + 18x3 + 36x2
6x6 + 18x3 + 36x2
8x5 + 24x3 + 48x2
8x6 + 24x3 + 48x2

Answer 1

8x2(x3 + 3x + 6)

8x5 + 25x3 + 48x2

Answer 2

option C is correct

`8x^5+24x^3+48x^2`

Explanation:

As per the statement:

The length(l), width(w) and height(h) of the rectangular prism are:

l = 4x

w = 2x

`h = x^3+3x+6`

We have to find volume.

Use the formula:

`V = lwh`

Substitute the given values we have;

`V = 4x \cdot 2x \cdot (x^2+3x+6)`

⇒
`V = 8x^2 \cdot (x^3+3x+6)`

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

then;

`V = 8x^5+24x^3+48x^2`

Therefore, the volume of the rectangular prism is,
`8x^5+24x^3+48x^2`