Question : Water flows at the rate of 10 meters per minute from a cylindrical pipe 5 mm in diameter. How long does it take to fill up a conical vessel whose diameter at the base is 30 cm and depth 24 cm?
Option 1: 28 minutes 48 seconds
Option 2: 51 minutes 12 seconds
Option 3: 51 minutes 24 seconds
Option 4: 28 minutes 36 seconds
Correct Answer: 28 minutes 48 seconds
Solution :
Given: Water flows at the rate of 10 meters per minute from a cylindrical pipe 5 mm in diameter.
Volume of water flown from cylindrical pipe of radius $r$ in 1 min = $\pi \times r^2\times \text{Rate of flow}$
Height of conical vessel = 24 cm
The radius of cylindrical pipe = 2.5 mm
Volume of water flown in 1 min = $\pi \times \frac{2.5}{10}\times \frac{2.5}{10}\times 1000= 62.5\pi$ cm
3
Volume of conical vessel of radius $r$ and height $h$ = $\frac{1}{3}\pi \times r^2h$
Volume of conical vessel = $\frac{1}{3}\pi \times 15 \times 15\times 24=1800\pi$ cm
3
Time required to fill the vessel
= $\frac{1800\pi}{62.5\pi}$
= 28.8 minutes
= 28 minutes 48 seconds
Hence, the correct answer is 28 minutes 48 seconds.
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