Question

a box has a length of 6X inches the width equal 1/3 the lamps in the height equals half the length of the volume equals 972 cubic inches what does x equal?

Answer 1

The length of the box is 6x inches

The width of the box is 1/3 of the length, that is:

1/3 * 6x = 2x inches

The height of the box is 1/2 of the length, that is:

1/2 * 6x = 3x inches

The volume of the box is 972 cubic inches.

The volume of a box (rectangular box) is given as:

V = L * W * H

where L = length, W = width, H = height

This means that:

V = 6x * 2x * 3x

`\begin{gathered} 972=36x^3 \\ \Rightarrow x^3\text{ = }(972)/(36) \\ x^3\text{ = 27} \\ \Rightarrow\text{ x = }\sqrt[3]{27} \\ x\text{ = 3} \end{gathered}`