a cube with an edge length of 10 is divided into two cuboids with integer edge lengths by a plane cut. then one of these two cuboids is divided into two cuboids with integer edge lengths by a second plane cut. what is the smallest possible volume of the largest of the three cuboids?
cuboid volume
- Thread starter nily123
- Start date
D
Deleted member 4993
Guest
Please show us what you have tried and exactly where you are stuck.
Please follow the rules of posting in this forum, as enunciated at:
Please share your work/thoughts about this problem.
Dr.Peterson
Elite Member
- Joined
- Nov 12, 2017
- Messages
- 16,087
It might help if you told us the context of the question. What have you been learning that this might be intended to use?
My first thought (after observing that all the cuts must be parallel to faces, and the thinnest anything can be is 1 unit) is that if we want the smallest possible size of the largest of three parts, then we want the parts to be similar in size. (Think of how you'd cut a cake if you want your brother, when he takes the largest, to get as little as possible.) We can't make them all be thirds of the cube, but I'd be aiming for something close.