Question

Water flows at the rate of $10$m per 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

R.E.F image

Volume of cone $=\frac{1}{3}\times r^{2}h$

$=\frac{1}{3}\times 3.14\times 20\times 20\times 24$

$=3.14\times 400\times 8$

$=10048c{m}^3$

Volume flown in $1$ min $=\pi r^{2}h$

$=3.14\times \frac{2.5}{10}\times \frac{2.5}{10}\times 1000c{m}^3$

$=196.25c{m}^3$

$\therefore$ time taken $=\frac{10048}{196.25}=51.2$

$\therefore$ 51 minutes and 2 seconds