Surface Area Equalizers

Geometry Level 2

As shown below, we can remove 8 unit cubes from 3 × 3 3\times 3 cube to obtain the same surface area.

Can we do better than that by removing more unit cubes from the start?

Note: A resulting solid does not have to be completely joint.

Yes. No.

Michael Huang by Michael Huang , 29, USA

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2 solutions

Parth Sankhe
Oct 9, 2018

You can remove every single cube except the corner ones and the body centre cube. The total surface area at the start was 6(9A) where A is area of one unit face, which can also be attained by taking 9 singular isolated cubes as each has a surface area of 6A.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Bivab Mishra
Oct 8, 2018

We can remove a cube from the inner most part. In that case the surface area still remains same.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Technically, if you remove the inner cube, it will increase the amount of surface area by 6. It really depends on how you define surface area.

Blan Morrison - 2 years, 8 months ago

You have to do better than 8 cubes from the start, that means remove more cubes not less.

Parth Sankhe - 2 years, 8 months ago

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