A water tank has the shape of a right circular cone with axis vertical and vertex downwards. Its semivertical angle is tan - 1 3 4 . Water is poured in it at a constant rate of 6 cubic meter per hour. The rate (in square meter per hour), at which the wet curved surface area of the tank is increasing, when the depth of water in the tank is 4 meters, is _______.

Step-by-step solution

Plotting the diagram we have, Now given, tan θ = 3 4 = r h and let water is poured at constant rate d V d t = 6 cubic meter per hour, Now we know that volume of cone is given by V = 1 3 π r 2   h = 1 3 π h 3 tan 2 θ = 9 π 48   h 3 = 3 π 16   h 3 by using  tan θ = 3 4 = r h Now differentiating above equation we get, ⇒ d V d t = 3 π 16 · 3 h 2 · d h d t = 6 ⇒ d h d t = 2 3 π m/hr Now, we know that curved surface area of cone i