If a cuboid of dimensions 32 cm $$\times$$ 12 cm $$\times$$ 9 cm is cut into two cubes of same size, what will be the ratio of the surface area of the cuboid to the total surface area of the two cubes?

For big cuboid,
l = 32 cm, b = 12 cm, h = 9 cm
Surface area = 2$$(l \times b + b \times h + h \times l)$$
= 2$$(32 \times 12 +12 \times 9 + 9 \times 32)$$ = 2$$(384 + 108 + 288)$$ = 1560
Assume that cuboid is melted to same size of cube so,
$$l \times b \times h = 2 \times a^3$$
$$32 \times 12 \times 9 = 2 \times a^3$$
$$1728 = a^3$$
a = 12 cm
Surface area of cube = $$6 \times 12^2$$ = 864
Ratio of the surface area of the cuboid to the total surface area of the two cubes = 1560 : $$2 \times 864$$ = 65 : 72