1. The difference between the outer and inner curved surface areas of a hollow cylindrical pipe is 44 square centimeters, and the length of the pipe is 14 cm. The volume of the material of the pipe is 99 cubic centimeters. Find the outer and inner radii of the pipe.

2. A vertical hollow cylindrical pipe made of iron has both ends open. Its height is 35 cm, the outer radius is 12 cm, and the inner radius is 10 cm. What is the volume of iron in the pipe in cubic centimeters?

3. A hollow metallic sphere has an inner radius of 3 cm and an outer radius of 5 cm. It is melted to form a solid right circular cylinder of height \(\frac{8}{3}\) cm. Find the diameter of the base of the cylinder.

4. A hollow vertical cylindrical iron pipe has an outer radius of 5 cm and an inner radius of 4 cm. If the total surface area of the pipe is 1188 square cm, what is the length of the pipe?

5. A right circular cylinder made of iron sheet is open at both ends. Its height is 42 cm, thickness is 1 cm, and its outer radius is 10 cm. Find the amount of iron used to make the cylinder.

6. A hollow iron cylinder of height 20 cm has an outer radius of 5 cm and an inner radius of 4 cm. This cylinder is melted and recast into a solid cone whose height is one-third of the original cylinder's height. Find the diameter of the base of the cone.

7. A hollow right circular cylinder has an outer diameter of 16 cm and an inner diameter of 12 cm. The height of the cylinder is 36 cm. If it is melted down, how many solid cylinders of diameter 2 cm and height 5 cm can be made from it?

8. A sphere and a right circular cylinder both have a radius of 3 cm. If their volumes are equal, what is the height of the cylinder?

9. 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.

10. A hollow cylinder with a height of 13 cm has an outer radius of 6.75 cm and an inner radius of 5.25 cm. It is melted to form a solid cylinder with a height of 6.5 cm. Find the radius of the solid cylinder.

11. The outer dimensions of a box with a lid are 12 cm in length, 10 cm in width, and 8 cm in height. The total inner surface area of the box is 376 square cm. If the walls of the box have equal thickness, what is their thickness?

12. The curved surface area of a right circular cylinder is 440 square cm, and its volume is 1540 cubic cm. Find the height of the cylinder.

13. If the height of a right circular cylinder is 14 cm and its curved surface area is 264 square cm, then find its volume.

14. A hollow sphere is made of lead sheet 1 cm thick and has an outer radius of 6 cm. If the sphere is melted and recast into a right circular cylinder with a radius of 2 cm, what will be the length of the cylinder? Let me know if you'd like the full solution too. I'm ready when you are.

15. A wooden box with a 5 cm thick lid is made from wooden planks. Its weight is 115.5 kg, and when filled with rice, it weighs 880.5 kg. The internal length and breadth of the box are 12 decimeters and 8.5 decimeters respectively, and the weight of rice per cubic decimeter is 1.5 kg. **(1) Calculate and write the internal height of the box.** **(2) At a rate of ₹1.50 per square decimeter, calculate the total cost to paint the outer surface of the box (excluding the base).**

16. If the height of a right circular cylinder is 14 cm and the curved surface area is 264 square cm, then what is the volume of the cylinder?

17. A vertical cylindrical tube made of iron is open at both ends. Its height is 42 cm, thickness is 1 cm, and the outer radius is 10 cm. Calculate the volume of iron used to make the tube.

18. A hollow vertical cylindrical iron pipe has an outer radius of 5 cm and an inner radius of 4 cm. If the total surface area of the pipe is 1188 square cm, calculate the length of the pipe.

19. A conical-shaped headgear made of shola has an outer base diameter of 21 cm. To cover its surface with foil, it costs ₹57.75 at a rate of 10 paise per square centimeter. Let us calculate the height and the slant height of the headgear.

20. The outer and inner radii of an iron pipe are 4 feet and 3 feet respectively, and its length is 20 feet. If the weight of 1 cubic foot of iron is 10 kilograms, what is the weight of the pipe?

(a) 4400 kg (b) 4040 kg (c) 4004 kg (d) 4000 kg

21. 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

22. The diagonal of a cuboid is √725 cm and its volume is 3000 cubic cm. The total surface area of the cuboid is 1300 square cm. Find the length, breadth, and height of the cuboid.

23. A conical-shaped head cap made of thermocol has a base diameter of 21 cm. Its upper surface is covered with foil, and the cost of covering is 10 paise per square centimeter, totaling ₹57.75. Find the height and slant height of the cap.

24. A hollow cylindrical iron pipe open at both ends has an inner radius and outer radius of 4 cm and 5 cm respectively. If the total surface area of the pipe is 1188 square centimeters, what is the length of the pipe?

25. If the height of a right circular cone is 14 cm and its curved surface area is 264 cm², what is the volume of the cone?

26. A solid cuboid has a length, width, and height ratio of \(4:3:2\), and its total surface area is \(468\) square cm. Determine the volume of the cuboid.

27. If the height and diameter of a right circular cylinder are equal, and its volume is 2156 cubic cm, then find the radius.

(a) 5 cm (b) 6 cm (c) 7 cm (d) 9 cm

28. The slant height of a right circular cone is 7 cm, and its total surface area is 147.84 square cm. Find the radius of its base.

29. The slant height of a right circular cone is 7 cm and its total surface area is 147.84 square cm. Find the radius of the base and the area of the base of the cone. Let me know if you'd like the full solution worked out as well. I'm happy to help.

30. The slant height of a right circular cone is 7 cm and its total surface area is 147.84 sq. cm. Find the radius of the base of the cone.