A large cube is painted blue and then 3 cuts are made on the X-axis, 6 cuts
are made on the Y-axis, and 5 cuts are made on the Z-axis. The cube is
then disintegrated. Calculate number of pieces with exactly 0 faces painted
blue.
Answers
40 pieces with exactly 0 faces painted
Step-by-step explanation:
3 cuts are made on the X-axis
=> Divided into 4 parts
6 cuts are made on the Y-axis
=> Divided into 7 parts
5 cuts are made on the Z-axis
=> Divided into 6 parts
Total Parts formed = 4 * 7 * 6 = 168
number of pieces with exactly 0 faces painted are parts = (4 - 2)(7-2)(6-2)
= 2 * 5 * 4
= 40
40 pieces with exactly 0 faces painted
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Answer:
40 pieces are exactly 0 faces painted blue.
Step-by-step explanation:
On a large cube the number of cuts are made on the X-axis = 3
The number of cuts are made on Y-axis = 6
The number of cuts are made on Z-axis = 5
Total number of pieces obtained with x cuts on X-axis, y cuts on Y-axis and z cuts on Z-axis
= (x+1) × (y+1) × (z+1)
= (3+1) × (6+1) × (5+1)
= 4 × 7 × 6
= 168 pieces
The cube was painted blue on its faces, the the number of pieces with exactly 0 faces painted blue
= (4-2) × (7-2) × (6-2)
= 2 × 5 × 4
= 40
40 pieces are exactly 0 faces painted blue.
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