A cuboid of sides 9 cm, 7 cm and 24 cm is melted to form a cube. What is the ratio of the total surface area of the cuboid to that of the cube?

19 : 18

Sides of a cuboid = 9 cm, 27 cm and 24 cm

Total surface area of cuboid, = 2(9 × 27 + 27 × 24 + 24 × 9) = 2(243 + 648 + 216) = 2214cm²

Volume of cuboid, = 9 × 27 × 24 = 5832 cm³.

Let, side of cube = s cm

According to problem,

= s³ = 5832

= s = 18

Side of cube = 18 cm

Total surface area of cube, = 6 × 18² = 1944

Required ratio, = 2214 ∶ 1944 = 41 ∶ 36