Question

The volume, of a rectangular solid with length L, width W, and height H is given by the formula V = LWH.

Answer 1

Answer:

$V(x) = 4x^3-34x^2+66x$

Step-by-step explanation:

Polynomials

We'll apply the polynomials to geometry.

The volume of a rectangular box can be calculated as

V = LWH

Where L is the length, W is the width, and H is the height of the box.

The figure shows the three dimensions as a function of the variable x:

W = 6 - 2x

L = 11 - 2x

H = x

Substituting in the formula of the volume:

$V(x) = (11-2x)(6-2x)(x)$

Multiplying the first two factors:

$V(x) = (66-22x-12x+4x^2)(x)$

Simplifying:

$V(x) = (66-34x+4x^2)(x)$

Multiplying by x:

$V(x) = 66x-34x^2+4x^3$

Reordering:

$\boxed{V(x) = 4x^3-34x^2+66x}$