InterviewSolution
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Water is flowing at the rate of 3 km/hr through a circular pipe of 20 cm internal diameter into a circular cistern of diameter 10 m and depth 2m. In how much time will the cistern be filled?1). 1 hour2). 1 hour 40 minutes3). 1 hour 20 minutes4). 2 hours 40 minutes |
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Answer» Let the time taken to fill the cistern be‘t’ hr. Given, Diameter of cistern is 10m and depth is 2m. We know that, Volume of CYLINDER = πR2 × h ⇒ Radius of cylinder = Diameter/2 = 5 m ∴ Volume of cylinder = π × 52 × 2 m3 = 50π m3 Given, Velocity of WATER = 3 km/hr = 3000 m/hr (? 1 km = 1000 m) Inner diameter of pipe = 20 cm ∴ Inner radius = 20/2 = 10 cm = 0.1 m (? 1m = 100 cm) ∴ Volume flow rate of water = π × (inner radius)2 × velocity of water = π × 0.12 × 3000 m3/hr = 30π m3/hr Now, ⇒Time taken to fill the cistern $(,t = \frac{{Volume\ of\ cistern}}{{Volume\ flow rate}})$ $(\Rightarrow t = \frac{{50{\rm{\pi }}}}{{30{\rm{\pi }}}}\ {\rm{hr}})$ ⇒ t = 1.67 hours Or, t = 1 hr 40 minutes |
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