a large 5x5x5 cube is made up of smaller 1x1x1 cubes. the large cube is painted blue on all sides. how many cu

Question

a large 5x5x5 cube is made up of smaller 1x1x1 cubes. the large cube is painted blue on all sides. how many cubes have 2 sides painted blue?


can you solve by algebra, make a rule so other qustions like this can be solved, and explain as your going along so i can get the idea??

thanks so much!

Answer 1

36

The 1 x 1 cubes that have blue on two sides are those that make up the edges, but not the corners (which are blue on three sides)

As the large cube is 5 x 5 x 5, the edges are each 5 of the smaller cubes long, including a corner cube at each end. This means each edge has 3 edge cubes with two blue sides and two corner cubes with 3 blue sides.

There are 12 edges in a cube. Each edge has 3 cubes that are blue on two sides

12 x 3 = 36

The rule for cubes is (y - 2) x 12 where y is the number of small cubes in a side (eg 5 as in your question)

And in case you need to know, the rule for the number of cubes with paint on just one side is:-

(y - 2)^2 x 6
(the number of cubes to an edge minus 2 then squared, which gives the number for one face of the cube, then multiplied by 6 because a cube has 6 faces)

Answer 2

36 rule is (length - 2) * 12 = answer (5 - 2) * 12 = 36 the 12 is becasue there are 12 edges on a dice the - 2 is by way of the fact 2 products on each and every side are corners with 3 factors painted blue.

Answer 3

36

Answer 4

Too rusty on my algebra to come up with the answer that way in a reasonable amount of time, but in my head, I say 24. I'll be curious to see if I'm right.

Edit - GLH is right. 36