Question

MO Question

Answer 1

A large cube is made of 1x1x1 small cubes. These small cubes are removed in a sequence of steps.
The first consists of removing all cubes with at least 2 visible faces. The second and subsequent steps use the same procedure.
- Beginning with 9x9x9 cube, what is the surface area of the object that remains after the first step? (i think the answer is 576 but not sure)
-Beginning with a 9x9x9 cube, how many small cubes are left after the third step.
Provide all working

Answer 2

@Kainui

Answer 3

@nincompoop @Preetha

Answer 4

my bad got 462 for first part is it right

Answer 5

@rational @thomaster @zepdrix

Answer 6

@bohotness @freckles

Answer 7

what is the surface area of a 9x9x9 cube before we remove any sides.
there are 6 sides to a cube. so 6 x9x9 = 486 total surface area

Answer 8

continue, i got them just wanna ensure theyre right

Answer 9

what is the surface area of a 9x9x9 cube before we remove any cubes.
there are 6 sides to a cube. so 6 x9x9 = 486 total surface area

Then we remove cubes that have at least two faces exposed , that means we remove all the corners and top row adjacent to the corner.

Answer 10

yes

Answer 11

it is difficult to draw but i get

Answer 12

So when I imagine removing cubes that will only take off really the edges and corners of the shape. So looking at it straight on gives something like this. So each of these also has faces on the edges of it, it's kind of the same exact thing as if we had started with a 7x7x7 cube and just put another 7x7x1 layer on each face. Since there are 4 sides to each of these with length of 7 all around for the "perimeter" areas.

So we have (7x7+4x7)x6=462 is what I'm getting for the surface area of the shape after removing in the first step.

Answer 13

I'm going outside to drink some coffee and decide what to do with my day, so I'm gone, I might be wrong but I just thought I should put that since it seemed like I was getting a different answer. Anywho good luck!

Answer 14

I like kianu's suggestion. start with a 7x7x7 cube and figure out the added surface area of adding 6 sides of 7x7x1 shapes