Question : A 9 cm solid metallic cube and a solid metallic cuboid having dimensions 5 cm, 13 cm, and 31 cm are melted and recast into a single cube, What is the total surface area (in cm2) of the new cube?
Option 1: 865
Option 2: 1176
Option 3: 1362
Option 4: 2744
Correct Answer: 1176
Solution :
Given: Side of cube = 9 cm
Cuboid length = 5 cm
Breadth = 13 cm
Height = 31 cm
Volume of cube = $\text{side}^3$ = $9^3$ = 729 cm
3
Volume of cuboid = length × breadth × height = 5 × 13 × 31 = 2015 cm
3
The volume of recast single cube
= Volume of solid metallic cube + Volume of solid metallic cuboid
= 729 + 2015
= 2744 cm
3
Side of Recast cube:
$\text{side}^3$ = 2744
⇒ side = 14 cm
Total surface area of cube = 6 × $\text{side}^2$ = 6 × 14 × 14 = 1176 cm
2
Hence, the correct answer is 1176.
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