A metal cube of edge 18 cm is melted to form three smaller cubes which are unequal in dimensions If ...........

Quantitative Aptitude (MTS) Mensuration 2D

A metal cube of edge 18 cm is melted to form three smaller cubes, which are unequal in dimensions. If the edges of two smaller

cubes are 9 cm and 15 cm, what is the surface area in (in cm²) of the third smaller cube?

This questions was previously asked in

SSC MTS 8th October 2021 Shift-1

1994

864

1728

486

- The large metal cube has a volume of \(18^3 = 5832 \, \text{cm}^3\).

- Two smaller cubes have edges of 9 cm and 15 cm.

- The volume of the cube with edge 9 cm is \(9^3 = 729 \, \text{cm}^3\).

- The volume of the cube with edge 15 cm is \(15^3 = 3375 \, \text{cm}^3\).

- The total volume of the two smaller cubes is \(729 + 3375 = 4104 \, \text{cm}^3\).

- Volume of the remaining cube is \(5832 - 4104 = 1728 \, \text{cm}^3\).

- The edge of the third cube is \(\sqrt[3]{1728} = 12 \, \text{cm}\).

- Surface area of the third cube is \(6 \times 12^2 = 864 \, \text{cm}^2\).

Option 2: 864

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