There is a cube in which one pair of opposite faces is painted red ; the second pair of opposite faces is painted blue and the third pair of opposite faces is painted green. This cube is now cut into 216 smaller but identical cubes .
how many cues are there with ONLY green and ONLY blue faces painted
Answers
Answer:
The cube root of 216 is 6.
Step-by-step explanation:
Imagine 216 cubes stacked 6 cubes wide, 6 deep and 6 high. You now have a large cube consisting of 216 smaller cubes. Spray paint that big All cubes internal to the large cube had no surfaces exposed to paint and can be eliminated. All cubes on the external sides with only a single surface exposed to the paint can be eliminated. We are left with a ‘hollow’ cube of edges and corners. Eliminate corners as they have 3 red sides, which leaves edges. Edges are the only locations with two sides exposed to the paint. With corners eliminated we have 4 small cubes per edge of the larger cube x 12 edges in a cube = 48 cubes with 2 red sides.
Answer:
There is a cube in which one pair of opposite faces is painted red ; the second pair of opposite faces is painted blue and the third pair of opposite faces is painted green. This cube is now cut into 216 smaller but identical cubes .How many cues are there with ONLY green and ONLY blue faces painted.
Step-by-step explanation:
- In the above question we are given with the information as-
- There is one cube in which one pair of opposite face of the cube is painted in color red.
- In such a way remaining two other faces of cubes which are opposite are painted in color blue and green.
- After this the cube is cut in such a way that 216 smaller cubes are formed, but the smaller cubes are all identical in size and shape.
- And we have to find out how many cubes are they which is only painted in green or blue.
- So there will be 64 cubes with at least two different colors on their faces.
Hence at least 64 cubes with at least two different colors on their faces.
#SPJ6.