Question
Water is running into a conical vessel, 15 cm deep and 5 cm in radius, at the rate of 0.1 cm2/sec. When the water is 6 cm deep, find at what rate is
(i) the water level rising?
(ii) the water surface area increasing?
(iii) the wetted surface of the vessel increasing?
Solution
Let V be the volume of the water in the cone i.e. the volume of the water cone CA 'B' at any time t.
Let CO' = h, O' A' = r and CA' = I.
Let α be the semi-vertical angle of the cone. CAB where CO = 15 cm, OA = 5 cm
CO = 15 cm
OA = 5 cm
Then, 
Also, 
...(2)
From (1) and (2), we get,
...(3)
Now, 
(ii) Let A be the water surface area at any time t. Then, A = 
(iii) Let S be the wetted surface area of the vessel at any time t. Then. S = 
Now, 
