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.
How many smaller cubes have at least one of their faces painted blue ?
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
Learn More:
A cube is painted blue on two adjacent faces. It is painted brown on ...
https://brainly.in/question/26094997
A large cube is painted blue and then 3 cuts are made on the X-axis ...
https://brainly.in/question/14108100
A solid cube is painted yellow, blue and black such that opposite ...
https://brainly.in/question/20955443
Answer:
50
Step-by-step explanation:
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 = 44
50 smaller cubes have at least one of their faces painted blue
plz mark as brainliast