Quantitative Aptitude Ques 2370

Question: Three solid iron cubes of edges 4 cm, 5 cm and 6 cm are melted together to make a new cube. $ 62cm^{3} $ of the melted material is lost due to improper handling. The area (in $ cm^{2} $ ) of the whole surface of the newly formed cube is

Options:

A) 125

B) 216

C) 294

D) 343

Show Answer

Answer:

Correct Answer: C

Solution:

  • Let edge of the new cube be a cm. According to the question, Volume of three small cubes $ -,62= $ Volume of big cube

$ \Rightarrow $ $ 4^{3}+5^{3}+6^{3}-62=a^{3} $

$ \Rightarrow $ $ a^{3}=64+125+216-62 $

$ \Rightarrow $ $ a^{3}=343 $
$ \Rightarrow $ $ a=7cm $

$ \therefore $ The whole surface area of newly formed cube $ =6a^{2}=6\times 49=294,cm^{2} $

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