Susan made a block with small cubes of volume 8 cubic cm to make a block, 3…
2024
Susan made a block with small cubes of volume 8 cubic cm to make a block, 3 small cubes long, 9 small cubes wide and 5 small cubes deep. She realizes that she has used more small cubes than she really needed. She realized that she could have glued a fewer number of cubes together to lock like a block with same dimensions, if it were made hollow. What is the minimum number of cubes that she needs to make the block?
- A.
135
- B.
71
- C.
114
- D.
31
Attempted by 380 students.
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Correct answer: C
Key idea: A hollow block with one-cube-thick walls is formed by taking the solid block and removing the interior block obtained by reducing each external dimension by 2 (one cube removed from each face).
Solid block cubes = 3 × 9 × 5 = 135
Interior removable block dimensions = (3 − 2) × (9 − 2) × (5 − 2) = 1 × 7 × 3
Number of interior cubes removed = 1 × 7 × 3 = 21
Minimum cubes needed for hollow block = 135 − 21 = 114
Answer: 114