1. 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?

2. 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?

3. 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?

4. The outer radius and inner radius of a hollow sphere made of iron are 21 cm and 7 cm respectively. If the weight of iron is 30 grams per cubic centimeter, what is the weight of the sphere?

(a) 2112.12 kg (b) 2212.21 kg (c) 1121.12 kg (d) 1122.21 kg

5. 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.

6. To make a hollow cylindrical pipe of uniform thickness, a solid iron sphere of radius 6 cm is melted. The pipe has a length of 18 cm and an outer radius of 10 cm. Find the thickness of the pipe.

7. 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.

8. 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.

9. A hollow cylindrical iron pipe is 6 meters long. Its internal and external diameters are 3.5 cm and 4.2 cm respectively. Calculate the volume of iron in the pipe. If the weight of iron is 5 kg per cubic decimeter, then find the total weight of the pipe.

10. A hollow cylindrical iron pipe, open at both ends, has a height of 2.8 meters. The inner circumference of the pipe is 4.6 decimeters, and it is made of 84.48 cubic decimeters of iron. Find the outer circumference of the pipe.

11. "A hollow cylindrical iron pipe is 6 meters long. The internal and external diameters of the pipe are 3.5 cm and 4.2 cm respectively. Calculate the amount of iron used in the pipe. If the weight of iron is 5 kg per cubic decimeter, calculate the weight of the pipe."

12. A circle with a radius of 10 cm has two parallel chords of lengths 4 cm and 6 cm. What is the distance between the two chords?

(a) \(\sqrt7(\sqrt3-\sqrt{12})\) cm (b) \(\sqrt3(\sqrt7+\sqrt{12})\) cm (c) \(\sqrt{13}(\sqrt{12}-\sqrt{7})\) cm (d) \(\sqrt{7}(\sqrt{13}+\sqrt{12})\) cm

13. 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.

14. A one-end open cylindrical pipe is 12 meters long and has a radius of 4.5 meters. What is the length of the longest rod that can be placed inside the cylinder?

15. 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.

16. A cylindrical water tank with a length of 10.5 meters is connected to a pipe with a diameter of 7 cm. If water flows through the pipe at a speed of 210 meters per minute and the tank empties in 45 minutes, what is the radius of the tank?

17. 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.

18. If a circle is centered at point 'O' with a radius of 13 cm and chord AB has a length of 10 cm, what is the distance from point 'O' to chord AB?

19. "A hollow cylindrical iron pipe is open at both ends. The external diameter of its mouth is 30 cm, the internal diameter is 26 cm, and the length of the pipe is 14.7 metres. If tar is applied to its entire surface at the rate of ₹2.25 per square decimetre, calculate and write the total cost."

20. 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.

21. In front of Anowar's house, there is a solid iron pillar with a cylindrical lower part and a conical upper part. The diameter of the base is 20 cm, the height of the cylindrical part is 2.8 meters, and the height of the conical part is 42 cm. If the weight of 1 cubic centimeter of iron is 7.5 grams, then calculate and write the total weight of the iron pillar.

22. 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.

23. The outer and inner radii of a hollow cylinder are 11 cm and 10 cm respectively, and its height is 14 cm. What is the volume of the metallic part of the cylinder?

(a) 880 cubic cm (b) 968 cubic cm (c) 88 cubic cm (d) 924 cubic cm

24. The radius of a circle is 13 cm and the length of a chord is 10 cm. What is the distance from the center of the circle to the chord?

(a) 12.5 cm (b) 12 cm (c) \(\sqrt{69}\) cm (d) \(\sqrt{24}\) cm

25. If a circle has a radius of 10 cm and two parallel chords of lengths 16 cm and 12 cm, what is the perpendicular distance between the two chords?

(a) \(14\sqrt3\) cm (b) 8 cm (c) 2 cm (d) 10 cm

26. A hollow sphere made of lead sheet with a thickness of 1 cm has an outer radius of 6 cm. After melting the sphere, a solid cylindrical rod with a radius of 2 cm is formed. What is the length of the rod?

27. If a right circular cylinder has a radius of 3 cm and a height of 4 cm, then what is the length of the longest rod that can be placed inside it?

28. If a right circular cone has a height of 12 cm and a volume of \(100\pi\) cubic cm, then what is the radius of the cone?

29. 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.

30. Given that the combined (weighted) mean of the following frequency distribution is 50 and the total frequency is 120, find the values of \( f_1 \) and \( f_2 \). | Class Interval | 0–20 | 20–40 | 40–60 | 60–80 | 80–100 | |----------------|------|--------|--------|--------|---------| | Frequency | 17 | \( f_1 \) | 32 | \( f_2 \) | 19 |