Question

The length of a box is four-and-a-half inches more than its height. The width of the box is seven inches more than it’s height. If the volume of the box is 4981.5 cubic inches, then what is the height of the box?

Answer 1

11.6 Inches

Explanation:

Let the dimensions of the box be l,w and h

The length of a box is four-and-a-half inches more than its height; written as:

• l=w+4.5

The width of the box is seven inches more than it’s height; written as:

• w=h+7

Making h the subject of the formula, we have:

• h=w-7

Volume of the box = 4981.5 cubic inches

Volume of a cuboid =lwh

Substituting the given values above:

`(w+4.5)(w)(w-7)=4981.5\\$Expanding\\w^3-2.5w^2-31.5w=4981.5\\w^3-2.5w^2-31.5w-4981.5=0\\$Solving the resulting cubic equation using a calculator\\w=18.6 inches (Every other value of w is in the complex plane)`

Therefore,

Height of the box, h=w-7=18.6-7=11.6 Inches