Question

Water flows at the rate of 10 m per mins from a cylindrical pipe of radius 2.5 mm. A conical vessel of diameter 40 cm and depth 24 cm is filled with water flowing from this pipe. The time taken to fill the conical vessel is:

• A. < 30 mins
• B. 30 < t < 50 mins
• C. 50 < t < 75 mins
• D. >75 mins

Answer 1

The correct option is C 50 < t < 75 mins

Area=$\pi$r${}^2$=6.25$\pi$

Rate of flow= ($\pi$r${}^2$x1000) mm${}^3$/min

=6250$\pi$ mm${}^2$/min

Volume of cone=$\frac{1}{3}$ $\pi$r${}^2$h = $\frac{1}{3}$ $\pi$ (200)${}^2$x 240 mm${}^3$

=80$\pi$x40000

=3200000$\pi$ mm${}^3$

Thus, total time taken is:

$\frac{\left(Volumeofconeinm{m}^3\right)}{\left(Rateofwaterflowinm{m}^3/min\right)}$ = 51.2min

Thus answer option (c) is correct.