Question : Three solid iron cubes of edges 4 cm, 5 cm, and 6 cm are melted to make a new cube. 62 cm3 of the melted material is lost due to improper handling. The area (in cm2) of the whole surface of the newly formed cube is:
Option 1: 294
Option 2: 343
Option 3: 125
Option 4: 216
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Correct Answer: 294
Solution :
Length of edges of cubes = 4 cm, 5 cm, and 6 cm.
Volume of the cube = a
3
Volume of all three cubes = 4
3
+ 5
3
+ 6
3
= 64 + 125 + 216
= 405 cm
3
Volume of all three cubes = Volume of the new cube + Volume of the melted material lost
⇒ Volume of new cube = 405 – 62 = 343 cm
3
⇒ Side of new cube = $\sqrt[3]{343}$ = 7 cm
So, the total surface area of the cube = 6a
2
= 6 × 7 × 7
= 294 cm
2
Hence, the correct answer is 294.
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