Question

HELP PLEASE


You have a 10 x 10 x 10 inch cube that is made up of little 1 x 1 x 1 inch cubes. You paint
the outside of the big cube red. How many of the little cubes have paint on at least one of
their sides?
(A) 456
(B)488
(C) 598
(D) 600
(E) 1000

Answer 1

First paint the top and the bottom and the outsides.

the bottom and the top are both 10x10 so in each case 100 little boxes get some color

the front is 10 x10 so that is 100 more little cubes, but we already counted the top and bottom row, so we remove 20 and now have 80

do the same for the back and get 80 more

now for the other two sides, we will have 100 little cubes again, but this time the top row and bottom row, AND the two side columns have paint, so we will only have 8*8

so we have 64 on each side

so we have

100+100+80+80+64+64 =?

Answer 2

488