Question

A conical vessel whose vertical angle is 90° is placed with its axis vertical and the vertex downwards. If water flows into it at the rate of 1 c.ft per minute, find the rate at which the level of water is rising when the height of the water in it is 2 ft.

Answer 1

Let h be the height, r be the radius and V be the volume of the water in the vessel at the time t. Vertical angle = 90° 

⇒ Semi vertical angle = 45°.

∴ The level of water is rising at the rate of 1/4π ft./minute.