Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube made from 27 unit cubes so that the surface area of the remaining solid is the same as the surface area of the original 3 by 3 by 3 cube? in how many different ways can this be done? worth 99 pts

I removed the 3 cubes from the centre of the big cube (the central column) obtaining an increase of the surface area with 10 units.

I removed a column (3 cubes) from one (any) corner of the big cube obtaining an increase with altogether 8 units of the surface area.

I removed another column, placed in the middle of a side, adjacent to the removed corner, obtaining the same surface area as at the beginning.

I removed a corner cube, not adjacent to those removed.

As example is sketched below: See picture attached.

a) 0.25x times 3. (could be wrong on equation.)

b) 2.25 pound of dark chocolate. (can i eat all the chocolate? plz? anyway, again, could be wrong, but i hope im right. all the chocolate together should be 5.25 pounds)

have a good day!

none of the above.

for one of the equations to be used in the process, there has to be a term in the equation since squared is .

since there is only a term in the first equation, we cannot derive a from completing the square.

solving with completing the square