Smallest possible volume

[Neil Nguyen]

Cube with edge length 10 is divided into two cuboids with integer edge lengths by a plane cut. Then one of these two cuboids is further divided into two cuboids with integer edge lengths by a second flat cut.

What is the smallest possible volume of the largest of the three cuboids?

Can someone help me?

 

[Deleted member 4993]

Cube with edge length 10 is divided into two cuboids with integer edge lengths by a plane cut. Then one of these two cuboids is further divided into two cuboids with integer edge lengths by a second flat cut.

What is the smallest possible volume of the largest of the three cuboids?

Can someone help me?

Assume that the first cut was made at a length x₁ - so that the new cuboid dimensions are now x₁ * 10 * 10 and (10-x₁) * 10 * 10 ..... continue...

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.

 

[Dr.Peterson]

Cube with edge length 10 is divided into two cuboids with integer edge lengths by a plane cut. Then one of these two cuboids is further divided into two cuboids with integer edge lengths by a second flat cut.

What is the smallest possible volume of the largest of the three cuboids?

Can someone help me?

I'm not sure this is a calculus problem at all. If the lengths didn't have to be integers, I think it's obvious what the minimum largest volume would be. So the entirety of the problem will be finding how close you can come to that with integers. That's mostly trial and error, or maybe just listing all cases.