Water flows through a cylindrical pipe of internal diameter 2 cm at a rate of…
2026
Water flows through a cylindrical pipe of internal diameter 2 cm at a rate of 6 cm per second into a cylindrical tank whose base radius is 100 cm. By how much will the water level rise in 15 minutes?
Answer: E. 0.54 cm — Calculate flow rate: Pipe radius (r) = 1 cm; flow rate = 6 cm/s. Volume flow per second = pi * r^2 * rate = pi * 1^2 * 6 = 6pi cm^3/s. Calculate total time in…
- A.
46 cm
- B.
50 cm
- C.
54 cm
- D.
62 cm
- E.
0.54 cm
Attempted by 36 students.
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Correct answer: E
Calculate flow rate: Pipe radius (r) = 1 cm; flow rate = 6 cm/s. Volume flow per second = pi * r^2 * rate = pi * 1^2 * 6 = 6pi cm^3/s.
Calculate total time in seconds: 15 minutes = 15 * 60 = 900 seconds.
Total volume of water: 6pi * 900 = 5400pi cm^3.
Calculate tank base area: Tank radius (R) = 100 cm. Area = pi * R^2 = pi * 100^2 = 10,000pi cm^2.
Calculate rise in height (h): h = Volume / Area = 5400pi / 10,000pi = 0.54 cm.
Final Answer: 0.54 cm