A conical water tank with its vertex at bottom has radius 20m and depth 20m.Water is being pumped into the tank at rate 40m^3/min.how fast is the level of the water rising when water is 8m deep? ( v=(pi x r² x h)/3 )

1 Answer
Jul 12, 2018

The level is rising at the rate of =0.199m/(mn)

Explanation:

The volume of water in the tank is

V=pi/3r^2h

The volumetric flow is q=(dV)/dt=40m^3mn^-1

In the cone

r/20=h/20

=>, r=h

Therefore,

V=pi/3r^2h=pi/3h^3

Differentiating wrt t

(dV)/dt=pi/3*3h^2*((dh)/dt)

h=8m

Plugging in the values

40=pi/3*3*8^2*((dh)/dt)

((dh)/dt)=40/(64pi)=5/(8pi)=0.199m/(mn)