1. Three solid copper spheres with radii of 3 cm, 4 cm, and 5 cm are melted and recast into a single solid larger sphere. Find the diameter of the larger sphere.

2. Three solid copper spheres with radii of 3 cm, 4 cm, and 5 cm are melted to form one larger solid sphere. Find the diameter of the larger sphere.

3. Three solid copper spheres with radii of 3 cm, 4 cm, and 5 cm are melted to form one larger solid sphere. Find the radius of the larger sphere.

4. Three solid copper spheres with radii of 3 cm, 4 cm, and 5 cm are melted to form a single larger solid sphere. Determine the diameter of the larger sphere.

5. Three solid copper spheres with radii of 3 cm, 4 cm, and 5 cm are melted to form one solid large sphere. Calculate the radius of the large sphere.

6. Three solid copper spheres with radii of 3 cm, 4 cm, and 5 cm are melted and used to form a single larger solid sphere. Find the radius of the larger sphere.

7. If two solid spheres with diameters of 1 cm and 6 cm are melted and recast into a hollow sphere with a thickness of 1 cm, then what is the outer surface area of the new hollow sphere?

8. If three solid spheres with radii of 3 cm, 4 cm, and 5 cm are melted and reformed into a larger sphere, what will be the radius of the new sphere?

9. The volume of a sphere is directly proportional to the cube of its radius. If three solid spheres with radii of 3 cm, 4 cm, and 5 cm are melted to form a new solid sphere, and there is no loss in volume during melting, then find the radius of the new sphere.

10. The volume of a sphere is directly proportional to the cube of its radius. Three solid spheres with diameters of \(1\frac{1}{2}\) m, 2 m, and \(2\frac{1}{2}\) m are melted and recast into a single solid sphere. Using the concept of proportionality, determine the diameter of the new sphere.

11. Two solid spheres with radii 1 cm and 6 cm are melted and recast into a hollow sphere of thickness 1 cm. Calculate and write the curved surface area of the new hollow sphere.

12. Two solid spheres with diameters of 20 cm and 6 cm are melted down, and the material is used to make a hollow sphere with a thickness of 1 cm. What is the inner radius of the hollow sphere.

13. Several coins, each with a diameter of 1.5 cm and thickness of 0.2 cm, are melted to form a solid vertical cylindrical rod with a height of 10 cm and diameter of 4.5 cm. Determine the number of coins used.

14. A cylindrical vessel with a radius of 12 cm contains some water. If 60 solid iron cones, each with a base diameter of 6 cm and a height of 4 cm, are completely submerged in the water, how much will the water level rise?

15. The volume of a sphere is in direct variation with the cube of its radius. If three solid spheres of radii 3 cm, 4 cm, and 5 cm are melted to form a single new solid sphere, and if there is no change in volume due to melting, then determine the diameter of the new sphere using the principle of variation.

16. A vertical circular cylindrical vessel with a diameter of 24 cm contains some water. If 60 solid cone-shaped iron pieces, each with a base diameter of 6 cm and height of 4 cm, are fully submerged in the water, calculate and write how much the water level will rise.

17. The radius of a solid right circular iron rod is 32 cm and its length is 35 cm. If the rod is melted and recast into solid cones each with a radius of 4 cm and height of 28 cm, calculate how many such cones can be made.

18. Two solid spheres with radii of 8 cm and 10 cm are melted to form a right circular cone with a height of 42 cm. What is the radius of the cone?

(a) 8 cm (b) 10 cm (c) 12 cm (d) 16 cm

19. Two solid spheres with radii of 1 cm and 6 cm are melted and recast into a hollow sphere with a thickness of 1 cm. Find the outer radius of the new hollow sphere and calculate its curved surface area.

20. A solid cylindrical iron rod has a base radius of 32 cm and a height of 35 cm. If the rod is melted and recast into solid cones, each with a radius of 8 cm and a height of 28 cm, how many such cones can be made?

21. A vertical hollow cylindrical pipe has an outer radius of 16 cm and an inner radius of 12 cm, with a height of 36 cm. If the pipe is melted and solid cylindrical rods are made from it, each with a diameter of 2 cm and a length of 6 cm, determine how many such solid rods can be produced.

22. Two solid spheres with radii of 1 cm and 6 cm are melted to form a completely hollow sphere with a radius of 5 cm. Determine the volume and curved surface area of the new sphere.

23. Three solid cubes have edge lengths of 3 cm, 4 cm, and 5 cm respectively. These cubes are melted and recast into a new solid cube. Write the length of an edge of the new cube.

24. A hollow sphere made of lead sheets with a thickness of 1 cm has an outer radius of 6 cm. If this sphere is melted and recast into a solid right circular rod with a radius of 2 cm, calculate the length of the rod.

25. "The volume of a sphere is directly proportional to the cube of its radius. Three solid spheres with diameters of 1½, 2, and 2½ meters are melted to form a new solid sphere. Find the diameter of the new sphere. (Assume volume remains the same before and after melting.)

26. Two solid spheres with radii 1 cm and 6 cm are melted to form a hollow sphere with an outer radius of 9 cm. Find the inner radius of the hollow sphere.

27. A solid lead sphere with a diameter of 12 cm is melted to form three smaller solid lead spheres. If the diameters of the smaller spheres are in the ratio 3 : 4 : 5, find the radius of each smaller sphere.

28. If three metallic cubes with edges measuring 3 cm, 4 cm, and 5 cm are melted and recast into a new cube, the length of the edge of the new cube will be –

(a) 6 cm (b) 7 cm (c) 8 cm (d) 9 cm

29. If a triangle similar to one with sides 4 cm, 6 cm, and 8 cm has its largest side measuring 6 cm, what is the length of the smallest side of that triangle?

(a) 4 cm (b) 3 cm (c) 2 cm (d) 5 cm

30. The radii of two solid iron spheres are \(r_1\) and \(r_2\) respectively. The spheres are melted and recast into a single solid sphere. What will be the radius of the resulting sphere?

(a) \((r_1^3+r_2^3)\) (b) \((r_1^3+r_2^3)^3\) (c) \((r_1+r_2)^3\) (d) \((r_1^3+r_2^3)^{\cfrac{1}{3}}\)