A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is t a n - 1 1 2 . Water is poured into it at a constant rate of 5 c u b i c m / m i n . Then the rate ( in m / m i n ) , at which the level of water is rising at the instant when the depth of water in the tank is 10 m ; is:

Step-by-step solution

The given water tank is of the shape shown by the diagram. The semi-vertical angle θ = tan - 1 1 2 ,     ⇒ tan θ = 1 2 Let at any time t   m i n , height of water level is h   m and radius of cone filled with water be r   m . Also, we have tan θ = r h ⇒ r h = 1 2 ⇒ r = h 2       . . . i Now, the volume of the water at time t   m i n in the cone is V = 1 3 π r 2 h On putting the value of r from the equation i , we get V = π 3 h 3