1. A tank measuring 21 decimeters in length, 11 decimeters in width, and 6 decimeters in depth is half-filled with water. If 100 solid spheres, each with a diameter of 21 centimeters, are submerged into the tank, by how many decimeters will the water level rise?

2. A vertical cylindrical gas jar with a diameter of 7 cm contains some water. If a solid iron right circular cylindrical piece with a diameter of 5.6 cm and height 5 cm is completely submerged in the water, calculate how much the water level will rise.

3. 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?

4. A tall gas jar with a diameter of 7 cm contains some water. If a solid cylindrical iron piece with a diameter of 5.6 cm and a height of 5 cm is completely submerged in the water, how much will the water level rise?

5. A conical vessel with a radius of 6 cm contains some water. Several solid spheres, each with a radius of 1.5 cm, are completely submerged in the water. How many such spheres are required to raise the water level by 2 cm?

6. A right circular drum has a radius of 21 cm and a height of 2i. A solid iron sphere has a diameter of 21 cm. Determine the ratio of the volumes of the drum and the solid iron sphere (neglecting the thickness of the drum). Now, if the drum is completely filled with water and the sphere is fully submerged and then removed, determine the new depth of the water in the drum.

7. A trough measuring 21 decimeters in length, 11 decimeters in width, and 6 decimeters in depth is half full of water. If 100 iron spheres, each with a diameter of 21 centimeters, are completely submerged in the trough, determine how much the water level will rise in decimeters.

8. "There is some water in a tall gas jar with a diameter of 7 cm. If a solid cylindrical iron piece with a diameter of 5.6 cm and a height of 5 cm is completely immersed in the water, calculate and write how much the water level will rise."

9. 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.

10. A tank that is 21 decimeters long, 11 decimeters wide, and 6 decimeters deep is half-filled with water. If 100 solid iron spheres, each with a diameter of 21 centimeters, are fully submerged in the tank, calculate how much the water level will rise (in decimeters).

11. A vertical cylindrical drum with a radius of 21 cm and height of 21 cm is completely filled with water. A solid sphere with a radius of 21 cm is taken and fully submerged into the drum, then removed. As a result, what is the new depth of water in the drum?

12. A solid lead sphere has a diameter of 14 cm. If this sphere is melted and reshaped into solid spheres with a radius of 3.5 cm, how many such spheres can be formed?

13. A tall gas jar with a diameter of 10 cm contains some water. A solid cylindrical iron piece with a diameter of 8 cm and a height of 5 cm is completely submerged in the water. Determine how much the water level rises.

14. Let us determine the amount of water displaced when a solid sphere with a diameter of 28 cm is completely submerged in water.

15. We take a vertical cylindrical drum with radius 21 cm and height 21 cm, and a solid iron sphere with a diameter of 21 cm. We calculate the ratio of the volumes of the drum and the solid iron sphere (neglecting the thickness of the drum). Next, we completely fill the drum with water and then fully immerse the sphere into it. Now, determine the new depth of water in the drum after the sphere is removed.

16. A hemispherical container with an inner radius of 9 cm is completely filled with water. This water is to be transferred into conical bottles, each having a diameter of 3 cm and a height of 4 cm. Calculate how many such bottles are needed to empty the container.

17. A solid copper cuboid of length 6.6 decimeters, width 4.2 decimeters, and thickness 1.4 decimeters is melted and recast into solid spheres, each with a diameter of 2.1 decimeters. Calculate how many such spheres can be made and how much metal will be in each sphere (in cubic decimeters).

18. A solid sphere with a radius of 3 cm is melted and recast into several small spherical balls, each with a diameter of 0.6 cm. How many such balls are formed?

(a) 1000 (b) 500 (c) 900 (d) 800

19. How many solid spheres of radius 5 mm can be made by melting a cylindrical iron rod that is 1 meter long and has a diameter of 4 cm?

20. A hemispherical vessel with an inner radius of 9 cm is completely filled with water. This water is poured into cylindrical bottles, each having a diameter of 3 cm and a height of 4 cm. How many such bottles are required to hold all the water?

21. How many spheres of 6 cm diameter must be dropped into a partially water-filled right circular cone of 16 cm diameter so that the water level rises by 9 cm?

22. A solid cylindrical iron rod has a cross-sectional diameter of 16 cm and a length of 1 meter. If this rod is melted and used to form right circular cones, each with a height of 4 cm and a base radius of 5 cm, how many such cones can be made?

23. 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.

24. If a pump set with a pipe of 14 cm diameter can irrigate 2,500 liters of water per minute, then how many kiloliters of water will it irrigate in an hour? (1 liter = 1 cubic decimeter)

25. "Four cylindrical concrete pillars each have a diameter of 17.5 cm and are to be plastered all around with a 3.5 cm thick layer of sand-cement mixture. If the height of each pillar is 3 metres, calculate and write how many cubic decimetres of mortar will be required."

26. "Four cylindrical concrete pillars each have a diameter of 17.5 cm and are to be plastered all around with a 3.5 cm thick layer of sand-cement mixture. If the mortar is prepared by mixing sand and cement in a 4:1 ratio, calculate and write how many cubic decimetres of cement will be required."

27. "A hollow right circular cylinder has an external diameter of 16 cm and an internal diameter of 12 cm. Its height is 36 cm. If it is melted and recast into solid cylinders, each with a diameter of 2 cm and a height of 6 cm, calculate and write how many such solid cylinders can be made."

28. The diameter of a solid lead sphere is 14 cm. If this sphere is melted, calculate how many solid spheres can be made from it, each having a radius of 3.5 cm.

29. If water flows through a pipe with an internal diameter of 5.6 cm at a rate of 200 meters per minute, how long will it take to fill \(\frac{5}{8}\) of a tank that is 2.8 meters long, 2.2 meters wide, and 1.6 meters deep?

30. A solid vertical cylindrical cone has both its diameter and height equal to 21 cm. Find the volume of the largest possible sphere that can be obtained from this cone. Also, determine the ratio of the volumes of the cone and the sphere.