The dimensions of a piece of iron in the shape of a cuboid are 256 cm × 135 cm × 50 cm. If it is melted and recast into a cube, find the surface area of the cube.

Correct option is C

Given:

Dimensions of cuboid =$$256\times 135\times 50$$​​

Formula Used:

Volume of cuboid = $$L \times B\times H$$​​

Where L,B,H are length, breadth and height of cuboid respectively

Volume of cube = $$a^{3}$$​​

Surface area of cube = $$6a^{2}$$​​

Where a is edge of cube

Solution:

If cuboid is recast into cube then volume is same

Volume = $$256\times 135\times 50 = 17,28,000 \ cm^{3}$$​​

Volume of cube is same, hence:

​$$a^{3} =17,28,000$$​​

​$$a= 120\ cm$$​​

Surface area of cube = $$6a^{2} = 6\times (120)^{2}$$​​

​$$= \bf 86400cm^{2}$$​​