Objects being fit into objects-question on volumes

[yo4561]

The All the Quant Book notes a common GMAT trick: "How many books each with a volume of 100 in3 can be packed into a crate with a volume of 5,000 in3
It is tempting to say 50 because (5,000/100=50) but this is INCORRECT because you do not know the exact dimensions of each book (one book could be 5 x 5 x 4 while another book can be 20 x 5 x 1). Without knowing the EXACT shapes of all of the books, you cannot tell whether they would all fit into the crate."

To clarify, wouldn't you also need to know the length, width and height of the crate and not just the length, width, and height of each book to determine sufficiency? For example, what if the crate is 1 by 1 by 5,000. then you may not be able to fit any books even if you know the length, width, and height of each book... no?

Should the takeaway be that you need to know BOTH the length, width, and height of an object you want to fit things into and the length, width, and height of the objects you are fitting into said thing, or does this only work when both objects are rectangular prisms? Let's say if you want to put spheres in a rectangular prism, would you only need to know the volume of the spheres but need to know the length, width, and height of the rectangular prism? Long story short... when do you need to know the length, width, and height of the objects given that you can have different 3D shapes beyond just rectangular prisms. Thank you so much!

[esledge]

Should the takeaway be that you need to know BOTH the length, width, and height of an object you want to fit things into and the length, width, and height of the objects you are fitting into said thing, or does this only work when both objects are rectangular prisms? Let's say if you want to put spheres in a rectangular prism, would you only need to know the volume of the spheres but need to know the length, width, and height of the rectangular prism? Long story short... when do you need to know the length, width, and height of the objects given that you can have different 3D shapes beyond just rectangular prisms. Thank you so much!

This is safe to say! If there's enough of a mismatch (even on one dimension), you might be able to fit 0 objects into the container. An empty carton (say, the type for copier paper) might not hold a fishing rod, despite the latter's small volume, due to the length mismatch.