Three cubes each having volume 1728 cm3 are placed one above the other What is the total surface are...........

Quantitative Aptitude (MTS) Mensuration 3D

Three cubes each having volume 1728 cm3 are placed one above the other. What is the total surface area of the resulting solid?

2304 cm3

2592 cm3

2160 cm3

2016 cm3

- Each cube has a volume of 1728 cm³.

- The side of each cube is calculated using the formula for the volume of a cube: side³ = 1728 cm³, so the side is 12 cm.

- When three cubes are stacked one on top of the other, the height becomes 3 × 12 = 36 cm.

- The resulting solid is a rectangular prism with dimensions 12 cm × 12 cm × 36 cm.

- Total surface area of this prism is calculated using the formula: 2(lw + lh + wh).

- Here, l = 12 cm, w = 12 cm, and h = 36 cm.

- Total surface area = 2(12×12 + 12×36 + 12×36) = 2(144 + 432 + 432) = 2×1008 = 2016 cm².

Option 4: 2016 cm²

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