Suppose sarah is trying to design a metal box (a rectangular prism), which will hold 450 cubic centimeters of liquid. the length of the box must be 2 times as large as the width. define a function j j that gives the height of the metal box, h h, measured in centimeters in terms of the width of the metal box, w w, measured in centimeters.

So, the volume of a container can also be thought of as the amount of liquid that the container is capable of holding. It follows that 450 = (length) (width) (height). The constraints of the problem say that the length of the box must be twice as large as the width, so it follows that j (height) = (2w) (w) (height) - 450. This then implies that j (height) = (2w^2) (height) - 450. In simpler terms, the height is defined as 450 / (2w^2), or j (w) = 450 / (2w^2).