A block of wood in rectangular form that is 4cm x 10cm x 11cm all surfaces of pink rose color. If the block of wood is cut into 440 cubes of 1cm × 1cm x 1cm each, how many cubes would have color pink rose?
Only cubes which are entirely internal to the block would have no pink on them. The block is 4 x 10 x 11cm so the size of the uncoloured "block" inside is 2 x 8 9cm. This equals 144 cubes. There are 440 cubes in total so 440 - 144 = 296 cubes will have at least one face coloured pink.
Specifically, there are: 8 corner cubes with 3 pink faces 76 edge cubes with 2 pink faces 212 face cubes with 1 pink face
384 cubes with at least on side with color pink rose
ReplyDeleteOnly cubes which are entirely internal to the block would have no pink on them. The block is 4 x 10 x 11cm so the size of the uncoloured "block" inside is 2 x 8 9cm. This equals 144 cubes. There are 440 cubes in total so 440 - 144 = 296 cubes will have at least one face coloured pink.
ReplyDeleteSpecifically, there are:
8 corner cubes with 3 pink faces
76 edge cubes with 2 pink faces
212 face cubes with 1 pink face