A solid cube of each side 8 cm, has been painted red, blue and black on pairs of opposite faces. it is then cut into cubical blocks of each side 2 cm. how many cubes have only one face painted red and all other faces unpainted
Answers
Answer: There are 8 cubes having one face painted red and all other faces unpainted.
Step-by-step explanation:
Each side of solid cube= 8cm
Each side of small solid cubes= 2cm
To calculate the number of smaller cubes having one face painted, we need to calculate the number of cubes present on the faces of bigger cube excluding the cubes present on edges.
Total number of cubes having one face painted and other face unpainted
= 6*{(8/2)-2}^2=6*4=24
But we need to calculate the cubes having one face painted with red and there are only two faces painted red.
So, by symmetry
Total number of cubes having one face painted with red and other face unpainted= 24/3=8
Answer:
Cubes have only one face painted red and all other faces unpainted =8
Step-by-step explanation:
The resulting cube image is attached with this answer.
It is given that,
A solid cube of each side 8 cm, has been painted red, blue and black on pairs of opposite faces.
It is then cut into cubical blocks of each side 2 cm. There are 4^3=64 Small cubes
There are 2 faces with red color.
From the figure we get only 4 cubes in each side have one side painted cube.
Therefore,cubes have only one face painted red and all other faces unpainted = 4 x 2 =8
