1. Water flows through a conical pipe with a radius of 3 cm and height of 12 cm at 4 m/s. Calculate:
(i) The volume of water discharged by the pipe in 1 minute.
(ii) The time, in minutes, it would take to fill a cylindrical tank with a height of 2 m and a radius of 1.5 m.
2. A cylindrical pipe with an internal diameter of 10 cm discharges water at a speed of 2 m/s. Calculate:
(i) The volume of water discharged in 10 minutes.
(ii) The height of water filled in a cuboidal tank measuring 5 m × 4 m × 3 m in 20 minutes.
3. Oil flows through a cylindrical pipe with a diameter of 5 cm and a speed of 6 m/s. Find:
(i) The volume of oil discharged in litres in half an hour.
(ii) The time taken to fill a hemispherical tank of diameter 2.5 m.
4. A hemispherical bowl with a radius of 7 cm is filled by water flowing from a pipe of internal diameter 2 cm at 3 m/s. Determine:
(i) The time taken to fill the bowl.
(ii) The volume of water discharged by the pipe in 15 minutes.
5. A pipe with an internal diameter of 8 cm discharges water at 10 m/s into a conical tank of height 2 m and base radius 1.5 m. Calculate:
(i) The time taken to fill the tank.
(ii) The volume of water discharged in 1 hour.
6. Water is flowing through a rectangular channel measuring 20 cm wide and 15 cm deep at a speed of 2 m/s. Find:
(i) The volume of water discharged in one minute.
(ii) The time taken to fill a tank measuring 6 m × 4 m × 2 m.
7. A cylindrical pipe with a radius of 3 cm discharges water at 2 m/s into a cuboidal tank of dimensions 5 m × 3 m × 2 m. Calculate:
(i) The time taken to fill the tank completely.
(ii) The height of water in the tank after 10 minutes.
8. Water flows through a circular pipe with a radius of 5 cm at a speed of 8 m/s. Calculate:
(i) The volume of water discharged in litres in 1 minute.
(ii) The time taken to fill a rectangular tank measuring 10 m × 5 m × 3 m.
9. A conical vessel with a radius of 10 cm and height of 15 cm is being filled by water flowing at 4 m/s through a pipe with a diameter of 2 cm. Find:
(i) The time required to fill the vessel.
(ii) The total volume of water discharged in 5 minutes.
10. Oil flows through a rectangular pipe measuring 12 cm by 10 cm at 5 m/s. Calculate:
(i) The volume of oil discharged in litres in 1 minute.
(ii) The height of oil in a tank measuring 4 m × 3 m × 2 m after 30 minutes.
11. A cylindrical pipe of diameter 6 cm discharges water into a cuboidal tank of dimensions 3 m × 2 m × 2 m. If the flow rate is 2 m/s, find:
(i) The volume of water discharged in 1 minute.
(ii) The time taken to fill the tank.
12. Water flows through a cylindrical pipe with an internal diameter of 14 cm at 3 m/s. Find:
(i) The volume of water discharged in 30 minutes.
(ii) The time required to fill a cylindrical tank with a radius of 2 m and height of 4 m.
13. A hemispherical bowl with a radius of 5 cm is filled by a pipe with a radius of 1 cm, flowing at 2 m/s. Calculate:
(i) The time taken to fill the bowl.
(ii) The volume of water discharged in 10 minutes.
14. Water flows through a rectangular channel measuring 50 cm by 40 cm at 1 m/s. Calculate:
(i) The volume of water discharged in litres in 2 minutes.
(ii) The time taken to fill a rectangular tank measuring 5 m × 4 m × 3 m.
15. A pipe with an internal diameter of 10 cm discharges water at a speed of 7 m/s into a tank with a hemispherical bottom and a radius of 3 m. Determine:
(i) The time taken to fill the hemispherical portion of the tank.
(ii) The volume of water discharged in 15 minutes.