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 = a3 Volume of all three cubes = 43 + 53 + 63 = 64 + 125 + 216 = 405 cm3 Volume of all three cubes = Volume of the new cube + Volume of the melted material lost ⇒ Volume of new cube = 405 – 62 = 343 cm3 ⇒ Side of new cube = $\sqrt[3]{343}$ = 7 cm So, the total surface area of the cube = 6a2 = 6 × 7 × 7 = 294 cm2 Hence, the correct answer is 294.
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Option 1: 484 cm2
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Option 2: 290 cm2
Option 3: 288 cm2
Option 4: 286 cm2
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Option 3: 428 cm2
Option 4: 584 cm2
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