| Water flows at the rate of 10 m/min from a cylindrical pipe 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40 cm and depth is 24 cm? [SSC (CGL) 2014] |
A) 51 min 12 s
B) 52 min 1 s
C) 48 min 15 s
D) 55 min
Correct Answer: A
Solution :
| Given, radius of pipe \[\frac{5}{2\times 10}=\frac{5}{20}\,\,cm\] |
| \[[\because 1\,\,cm=10\,\,mm]\] |
| Height of pipe \[=1000\,\,cm\] |
| Radius of vessel \[=20\,\,cm\] and height \[=24\,\,cm\] |
| Volume of water flow in one minute from cylindrical pipe |
| \[=\pi {{\left( \frac{5}{20} \right)}^{2}}\times 1000=\frac{125}{2}\pi \,\,c{{m}^{3}}\] |
| and volume of conical vessel |
| \[=\frac{1}{3}\pi \,\,{{(20)}^{2}}\times 24=3200\,\,\pi \,\,c{{m}^{3}}\] |
| \[\therefore \]Required time \[=\frac{3200\pi \times 2}{125\,\,\pi }=51\frac{1}{5}\] or \[51\,\,\min 12\,\,s\] |
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