1yes i have also had the same approach... thank you
Given a cube in which you can put two massive spheres of radius 1.
What's the smallest possible value of the side - length of the cube?
Prove that your answer is the best possible.
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4 Answers
62This seems to be an interesting question..
Let us assume that we have oriented the cube such that one vertex is on the origin and the sides are parallel to the coordinate axis
The x coordinate of one wall is 0 and the other wall is a
The y coordinate of one wall is 0 and the other wall is a
The z coordinate of one wall is 0 and the other wall is a
The radius of the circle is 1 each.
Clearly the center of the sphere will have one coordinate at a distance of 1 from one of the walls!
So let one of the spheres have a center at x=1
now if the other sphere has its center at x=a-1 or y=a-1 or z=a-1 or a combination of these....
Now can you fill the proof... I have a feeling that the proof is almost done.. do you?