Question
Download Solution PDF3 solid cubes whose sides are 3 m, 4 m and 5 m, respectively, are melted to form a new cube. The total surface area of the new cube will be ________.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Side lengths of the three cubes = 3 m, 4 m, and 5 m
Concept:
When cubes are melted and reshaped into a new cube, the volume remains the same. The total surface area of a cube is 6 × side2 .
Solution:
Volume of new cube = Sum of volumes of individual cubes = 33 + 43 + 53 = 27 + 64 + 125
Volume of new cube = 216 m3
Side of new cube = Cube root of volume of new cube = Cube root of 216 = 6 m
Total surface area of new cube = 6 × (side of new cube)2
⇒ Total surface area = 6 × 62
⇒ Total surface area = 216 m2
Therefore, the total surface area of the new cube is 216 m2.
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