SOLUTION: Twenty-seven congruent cubes are glued together to form a larger cube. All six faces of the larger cube are painted pink. What is the product of the number of small cubes that have

Question 238729: Twenty-seven congruent cubes are glued together to form a larger cube. All six faces of the larger cube are painted pink. What is the product of the number of small cubes that have a single pink face and the number of small cubes that have three pink faces?
Answer by JimboP1977(311) (Show Source): You can put this solution on YOUR website!
The way I would attack this problem is to actually draw the cube which comprises of 3 layers of 9 small cubes all together.
Then looking at the cube you can count the small cubes that have a one face painted and those that have three.
Looking at the larger cube you can see that the the middle smaller cube of each face of the larger cube has one face coloured. So that is 6 small cubes with 1 face.
The small cubes with three faces coloured are the corner ones of the larger face. So that is 8 cubes.
So the answer is 6*8 = 48.
There may be a more mathematical way of doing this that other tutors can elabourate on...
Does this help?
RELATED QUESTIONS
Twenty-seven congruent cubes are glued together to form a larger cube. All six faces of... (answered by Theo)

Twenty seven unit cubes are each coloured completely blue or completely yellow. All... (answered by ikleyn)

A large cube is painted red and then cut into 1000 congruent small cubes. How many of... (answered by macston)

A 6x6x6 cube is constructed of 1x1x1 cubes. The faces of the large cube are then painted. (answered by robertb)

Please help me to get how to solve this problem. Thank you! Here it is... There are... (answered by scott8148)

i need help with this question: One thousand cubes are arranged to form a large cube.... (answered by Edwin McCravy)

if a cube of length 16 cm is painted on all faces in blue then cut up into 2cm cube ,... (answered by greenestamps)

Below is 4*4*4 cube. Matuk painted all six faces purple. when it dried he separated the... (answered by ikleyn,greenestamps)

Pls help me with this qn: One thousand cubes are arranged to form a large cube. All the... (answered by checkley71)