Question

Water flows at the rate of 10m/min through a cylindrical pipe of 5mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm?

Answer 1

Radius of the pipe $=\frac{5}{2}$ mm $=\frac{5}{2}\times \frac{1}{10}$ cm $=\frac{1}{4}$ cm [1mm = 1/10 cm]

Speed of water = 10 m/min = 1000 cm/min [ 1m = 100 cm]

Volume of water that flows in 1 minute $=\pi r^{2}h=\frac{22}{7}\times \frac{1}{4}\times \frac{1}{4}\times 1000=\frac{1375}{7}c{m}^3$
[volume of cylinder= Π r2 h]

Radius of conical vessel $=\frac{40}{2}=20$cm;

Depth = 24 cm

Therefore, Capacity of the vessel $=\frac{1}{3}\times \pi r^{2}h$

$=\frac{1}{3}\times \frac{22}{7}\times 20\times 20\times 24=\frac{70400}{7}c{m}^3$

Therefore, Time required to fill the vessel = capacity of the vessel / volume of water flowing per minute

$=\frac{\frac{70400}{7}}{\frac{1375}{7}}=\frac{70400}{7}\times \frac{7}{1375}=\frac{256}{5}$ minutes = 51 min 12 sec