rectangular solids with cylinders in them

[Grumppee17]

Hi all,

I'm having a hard time trying to understand dimensions of a rectangular solid. For instance, if they give you a box with the dimensions 6 by 8 by 10.....is that length, width and height respectively? Also...when you are asked to find the radius of a cylinder that's supposed to go in this box......I don't understand how you're supposed to do that. I know you are supposed to take the max possible height of box and smaller dimension of box? Totally lost.. Thanks in advance.

[StaceyKoprince]

If they don't specify, the 6x8x10 can apply to any of the dimensions (length, width, height).

For cylinder in the box questions, they'll either tell you the orientation (relative to the dimensions of the box) or they'll ask you something like "what is the maximum possible radius (or volume) of a cylinder" that is put inside a specific box. For this, you need to know the various formulas for cylinders.

I recommend you go find a box and grab a can of soup (or something similar) and play around with the two to understand what's going on. In order to maximize the volume of the cylinder, for example, you want to maximize the dimension in the volume formula that has the biggest impact. For cylinders, volume = h*pi*r^2, so r (radius) has the biggest impact on volume (since it gets squared).

So I want to maximize the radius. Play with that soup can and figure out the orientation that would allow you to maximize the radius. Essentially, you want to match the circular face of the can with the face of the box that contains the largest two dimensions (eg, 8 and 10, in the above example). The maximum diameter is then the smaller of the two dimensions (in this case 8) - again, prove this to yourself with your box and can. And the max radius is just half of that max diameter.