Question

Water is being poured at the rate of 36 m³/sec in to a cylindrical vessel of base radius 3 meters. Find the rate at which water level is rising

Answer 1

Let h be the height of water level, r be the radius of the base and V be the volume of the cylindrical vessel.

Then, r = 3 metres, `("dV")/("dT")`

= 36 m³/sec

V = πr²h

= π(3)²h

= 9πh

Differentiating w.r.t.t, we get

`("dV")/("dt") = 9pi*("dh")/("dt")`

∴ `("dh")/("dt") = (("dV")/("dt")) xx 1/(9pi)`

= `36/(9pi)`

= `4/pi` m/sec

Thus, water level is rising at the rate of `4/pi` m/sec.