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      Question

      Three solid cubes of metal have sides 6 cm, 8 cm and 10

      cm, respectively. They are melted to form a new cube. What is the surface area of this new cube?
      A 915 cm² Correct Answer Incorrect Answer
      B 864 cm² Correct Answer Incorrect Answer
      C 950 cm² Correct Answer Incorrect Answer
      D 812 cm² Correct Answer Incorrect Answer

      Solution

      Volume of the first cube = 63 = 216 cm3 Volume of the second cube = 83 = 512 cm3 Volume of the third cube = 103 = 1000 cm3 Total volume = 216 + 512 + 1000 ⇒ Total volume = 1728 cm3 Let the side of the new cube be x cm. Volume of the new cube = x3 Since the volume of the new cube is equal to the total volume of the three cubes: x3 = 1728 ⇒ x = 12 cm Surface area of the new cube = 6 × 122 ⇒ Surface area = 6 × 144 ⇒ Surface area = 864 cm2 The surface area of the new cube is 864 cm2.

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