cube of dimensions 10” is painted red, blue and green respectively, on the three sets of opposite faces. The cube is then cut into 104 smaller cubes, some with 4” dimensions and some with 2” dimensions. Two of the cubes of dimensions 4” have only one of their faces painted red. The remaining cubes of dimensions 4” have only one of their faces painted green.
How many smaller cubes have at least one of their faces painted blue ?
Please answer asap..
Answers
Given : A cube of dimensions 10" is painted red, blue and green respectively, on the three sets of opposite faces. The cube is then cut into 104 smaller cubes, some with 4” dimensions and some with 2"
dimensions. Two of the cubes of dimensions 4" have only one of their faces painted red. The remaining cubes of dimensions 4" have only one of their faces painted green.
To Find : How many smaller cubes have at least one of their faces painted blue ?
Solution:
smaller cubes with 4” dimensions = a
Volume = 64a
smaller cubes with 2” dimensions = 104-a
Volume = 8*(104 - a) = 832 - 8a
Total Volume = 10 * 10 * 10 = 1000
64a + 832 - 8a = 1000
=> 56a = 168
=> a = 3
cubes of dimensions 4" = 3
2 are painted Red
1 is painted Green
No 4'' on Blue
Hence Blue Painted are only 2''
2'' cubes on one face = 10 * 10 / 2 * 2 = 25
on 2 Faces = 2 * 25 = 50
50 smaller cubes have at least one of their faces painted blue
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