Question

Question 5
Water flows at the rate of 10m/minute through a cylindrical pipe 5 mm 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

Given, speed of water flow $=10mmi{n}^{-1}=1000cm/min$
$\therefore$ Radius of the pipe $=\frac{5}{10\times 2}=0.25cm$
$\therefore$ Area of the face of $pipe=\pi r^2=\pi r^2=\frac{22}{7}\times (0.25{)}^2=0.1964c{m}^2$
Also, given diameter of the conical vessel = 40 cm
$\therefore$ Radius of the conical vessel $=\frac{40}{2}=20cm$
And depth of the conical vessel $=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \frac{22}{7}\times (20{)}^2\times 24=\frac{211200}{21}=10057.14c{m}^3$
$=Requiredtime=\frac{Volumeoftheconicalvessel}{Areaofthefaceofpipe\times Speedofwater}=\frac{10057.14}{0.1964\times 10\times 100}=51.20min=51min\frac{20}{100}\times 60s=51min12s$