| Three solid iron cubes of edges 4 cm, 5 cm and 6 cm are melted together to make a new cube. \[62\text{ }c{{m}^{3}}\]of the melted material is lost due to improper handling. The area (in\[c{{m}^{2}}\]) of the whole surface of the newly formed cube is |
A) 125
B) 216
C) 294
D) 343
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 |
| \[\Rightarrow \]\[{{4}^{3}}+{{5}^{3}}+{{6}^{3}}-62={{a}^{3}}\] |
| \[\Rightarrow \]\[{{a}^{3}}=64+125+216-62\] |
| \[\Rightarrow \]\[{{a}^{3}}=343\]\[\Rightarrow \]\[a=7\text{ }cm\] |
| \[\therefore \] The whole surface area of newly formed cube |
| \[=6{{a}^{2}}=6\times 49=294\,c{{m}^{2}}\] |
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