Question : A solid sphere made of wax of radius 12 cm is melted and cast into solid hemispheres of radius 4 cm each. Find the number of such solid hemispheres.

Option 1: 54

Option 2: 27

Option 3: 14

Option 4: 28

Question : Three spherical balls of radius 2 cm, 4 cm, and 6 cm are melted to form a new spherical ball. In this process, there is a loss of 25% of the material. What is the radius (in cm) of the new ball?

Option 1: 6

Option 2: 8

Option 3: 12

Option 4: 16

Question : A solid metallic sphere of radius x cm is melted and then drawn into 126 cones each of radius 3.5 cm and height 3 cm. There is no wastage of material in this process. What is the value of $x$?

Option 1: 10.5

Option 2: 3.5

Option 3: 7

Option 4: 21

Question : A solid metallic sphere of radius 8.4 cm is melted and recast into a right circular cylinder of radius 12 cm. What is the height of the cylinder? (Your answer should be correct to one decimal place.)

Option 1: 6.5 cm

Option 2: 5.5 cm

Option 3: 7.0 cm

Option 4: 6.0 cm

Question : A 9 cm solid metallic cube and a solid metallic cuboid having dimensions 5 cm, 13 cm, and 31 cm are melted and recast into a single cube, What is the total surface area (in cm²) of the new cube?

Option 1: 865

Option 2: 1176

Option 3: 1362

Option 4: 2744