 Hello and welcome to the session. In this session we discuss the following question which says water flows at the rate of 14 cm per minute through a cylindrical pipe 3 cm in radius. How long would it take to fill a conical vessel whose diameter at the surface 18 cm and depth 14 cm? We know that the volume of a cylinder is equal to pi r square h r is the radius of the base of the cylinder h is the height of the cylinder and the volume of a cone is equal to 1 upon 3 pi r square h where this r is the radius of the base of the cone h is the height of the cone. This is the key idea to be used for this question. Now we move on to the solution. Now the radius of the cylindrical pipe that is r1 is equal to 3 cm as given in the question. Now the rate of flow of water in the cylindrical pipe is given as 14 cm per minute. That means the height of the cylindrical pipe the h1 is equal to 14 cm. So now volume of the cylindrical pipe say v1 is equal to pi r1 square into h1 that is equal to pi 3 square into 14 cm cube. Next we consider the radius of the conical vessel say r2 is equal to as given in the question the diameter is 18 cm so obviously the radius would be 18 upon 2 that is 9 cm. Then the height of the conical vessel say h2 is given as 14 cm. So the volume of the conical vessel say v2 is equal to 1 upon 3 pi r2 square into h2 that is equal to 1 upon 3 into pi into 9 square into 14 cm cube. Now this volume of the cylindrical pipe can also be said as the volume of the water that flows through a cylindrical pipe in 1 minute is equal to pi 3 square into 14 cm cube. Now that we are required to find out how long would it take to fill a conical vessel whose diameter is 18 cm and depth is 14 cm. So for this we say that the required time is equal to the volume of the conical vessel that is v2 upon the volume of the water that flows through the cylindrical pipe in 1 minute that is pi 3 square into 14. Now we have got v2 as 1 upon 3 into pi into 9 square into 14 and this upon pi into 3 square into 14. Now this pi in pi cancels 14 and 14 cancels this is equal to 1 upon 3 into 9 into 9 upon 3 into 3. Now 3 3 times is 9 this 3 and this 3 cancels and 3 3 times is 9 so this is equal to 3 minutes. This is the required time. So the time required to fill up the conical vessel is equal to 3 minutes. So our final answer is 3 minutes. This completes this session. Hope you understood the solution for this question.