7. A company uses rectangular boxes to package small electronic components for shipping. The box that is currently used can contain 500 of one type of component. The company wants to package twice as many pieces per box. Michael thinks that the box will hold twice as much if its dimensions are doubled. Shawn disagrees and says that Michael’s idea provides a box that is much too large for 1,000 pieces. Explain why you agree or disagree with one or either of the boys. What would you recommend to the company?

If you have a cube or a rectangle prism, and you double its dimensions you are left with a box that is 8 times as big as the first one, as we are talking about volume and volume is elevating things to the cube. In order to double the volume, you just need to double one of its dimensions, and you will get double the volume in the box, for example, double its height, or the length.