Question : A solid metallic cuboid of dimensions 18 cm × 36 cm × 72 cm is melted and recast into 8 cubes of the same volume. What is the ratio of the total surface area of the cuboid to the sum of the lateral surface areas of all 8 cubes? 

Option 1: 4 : 7

Option 2: 7 : 8

Option 3: 7 : 12

Option 4: 2 : 3

Question : The radius of a large solid sphere is 14 cm. It is melted to form 8 equal small solid spheres. What is the sum of the total surface areas of all 8 small solid spheres? (use $\pi=\frac{22}{7}$)

Option 1: 3648 cm²

Option 2: 4928 cm²

Option 3: 4244 cm²

Option 4: 4158 cm²

Question : The areas of three adjacent faces of a cuboidal solid block of wax are 216 cm², 96 cm² and 144 cm². It is melted and 8 cubes of the same size are formed from it. What is the lateral surface area (in cm²) of 3 such cubes?

Option 1: 648

Option 2: 432

Option 3: 576

Option 4: 288

Question : The sum of the length, breadth, and height of a cuboid is 20 cm. If the length of the diagonal is 12 cm, then find the total surface area of the cuboid.

Option 1: 364 cm²

Option 2: 256 cm²

Option 3: 356 cm²

Option 4: 264 cm²

Question : Three cubes of equal volume are joined end to end. Find the surface area of the resulting cuboid if the diagonal of the cube is $6 \sqrt{3} \mathrm{~cm}$.

Option 1: 509 cm²

Option 2: 504 cm²

Option 3: 516 cm²

Option 4: 512 cm²