Question : A spherical ball of lead, 3 cm in diameter, is melted and recast into three spherical balls. The diameters of two of these balls are $\frac{3}{2}$ cm and 2 cm, respectively. Find the diameter of the third ball.

Option 1: 2.1 cm

Option 2: 3.3 cm

Option 3: 3 cm

Option 4: 2.5 cm

Question : The sum of the curved surface area and the total surface area of a solid cylinder is 2068 cm². If the radius of its base is 7 cm, then what is the volume of this cylinder? (use $\pi=\frac{22}{7}$)

Option 1: 2060 cm³

Option 2: 2480 cm³

Option 3: 3080 cm³

Option 4: 2760 cm³

Question : The curved surface area of a solid hemisphere is 22 cm². What is the total surface area of the hemisphere? (use $\pi=\frac{22}{7}$)

Option 1: 66 cm²

Option 2: 44 cm²

Option 3: 33 cm²

Option 4: 30 cm²

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 : Three solid metallic spheres of radii 1 cm, 6 cm, and 8 cm, respectively, are melted and recast into a single solid sphere. The radius of the new sphere formed is:

Option 1: 9.0 cm

Option 2: 5.9 cm

Option 3: 7.7 cm

Option 4: 8.5 cm