- A95
- B34
- C94
- D125
Step-by-Step Solution
The cuboid is cubes. The smallest cube containing it has edge 5: . Needed: .
Answer: A) 95
Arjun built this cuboid from unit cubes. He wants to add more unit cubes to turn it into the smallest solid cube that contains it. How many more unit cubes does he need?
Class 8Cubes and Cube RootsCubes and Roots
Key idea: Cube root by prime factorisation
**Step 1**: factorise into primes.
**Step 2**: group the prime factors into TRIPLES (three of the same).
**Step 3**: take ONE factor from each triple — their product is the cube root.
Example: ∛216. . So ∛216 = 6.
Example: ∛13824. . So ∛13824 = 24.
If any prime doesn't form a complete triple, the number isn't a perfect cube.
**Step 2**: group the prime factors into TRIPLES (three of the same).
**Step 3**: take ONE factor from each triple — their product is the cube root.
Example: ∛216. . So ∛216 = 6.
Example: ∛13824. . So ∛13824 = 24.
If any prime doesn't form a complete triple, the number isn't a perfect cube.
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