A cuboid whose sides are 8 cm, 27 cm and 64 cm is melted to form a new cube. What is the respective ratio of the total surface area of the cuboid and cube?

307 : 216

The volume of the new cube = Volume of cuboid 

⇒  8 x 27 x 64    =  (side)³

⇒  side  = \(\sqrt[3]{8 \times 27 \times 64 }\)

             = 2 x 3 x 4 = 24

Surface area of cuboid = 2(lb + bh + lh) 

                                 = 2(8x27 + 27x64 + 64x8)

                                 = 2 x(216 +  1728 +  512)

                                 =  4912 cm²

Surface area of cube  = 6(side)²

                                = 6 x 24 x24 = 3456 cm²

Ratio = 4912 : 3456 = 307 : 216