A cuboid which sides 6 cm, 9 cm and 32 cm is melted to form a new cube. What is the ratio between the total surface area of the cuboid and that of the cube?

Given Length = 6 cm breadth = 9 cm height = 32 cm (of the cuboid)

Volume of both cube and cuboid will be same,

We know that volume of a cuboid = length x breadth x height and volume of the cube = a$$^{3}$$

$$\therefore$$ 6 x 9 x 32  = a$$^{3}\Rightarrow$$ a = 12

Now, surface area of the cuboid is given by,

2(lb + bh + hl) = 2(54 + 288 + 192) = 2 x 534 = 1068

 surface area of the cube is given by,

6 a$$^{2}$$ = 6 (12)$$^{2}$$ = 864

Ratio of surface area of cuboid and surface area of cube = 1068 : 864 = 89 : 72

Hence, option D is the correct answer.