Bob has four square plastic recycling boxes that she wants to put on a shelf in her garage. How low does the shelf ne

Question

Bob has four square plastic recycling boxes that he wants to put on a shelf in his garage. If the top opening of the box is 432 in^2, how low does the shelf need to be? Leave your answer in radical form. Thank you for any of your help

Answer 1

Bob has four square plastic recycling boxes that he wants to put on a shelf in his garage. If the top opening of the box is 432 in^2, how low does the shelf need to be? Leave your answer in radical form.

 

A square with an area of 432 sq in has sides of √432, or √(16 * 9 * 3), or 4 * 3 * √3, or 12√3.

 

The problem does not say if the boxes are cubes, but I must assume so or there is no way to determine the height.

 

So the box is 12√3 high, and the shelf must be that far below the ceiling if the boxes are stacked next to each other on the shelf. If they are stacked on top of one another, the shelf must be 4 times that, or 48√3.