Answer» Correct Answer - Option 4 : 218
The correct answer is 218. Let us interpret all the options as per the given information: First option: It is given that 125 small but identical cubes have been put together to form a large cube If we add 208 more cubes, the total number of cubes becomes 333. 333 is not a perfect cube. It is short of 10 more cubes to form a perfect cube. If we add 10 more cubes, then the total becomes 343 which is a perfect cube. Hence, the first option is incorrect.
Second option: It is given that 125 small but identical cubes have been put together to form a large cube If we add 212 more cubes, the total number of cubes becomes 337. 337 is not a perfect cube. It is short of 6 more cubes to form a perfect cube. If we add 6 more cubes, then the total becomes 343 which is a perfect cube. Hence, the second option is incorrect.
Third option: It is given that 125 small but identical cubes have been put together to form a large cube If we add 254 more cubes, the total number of cubes becomes 379. 379 is not a perfect cube. It is short of 133 more cubes to form a perfect cube. If we add 133 more cubes, then the total becomes 512 which is a perfect cube. Hence, the third option is incorrect.
Fourth option: It is given that 125 small but identical cubes have been put together to form a large cube If we add 218 more cubes, the total number of cubes becomes 343. 343 is a perfect cube. Thus, we will be able to form a perfect cube from the given 125 identical cubes if we add 218 more cubes to it. Hence, the fourth option is correct.
Hence, the correct answer is 218.
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