 Hello and welcome to the session. In this session we discussed the following question which says water is flowing at the rate of 5 km per hour through a pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44 m wide, determine the time in which the level of the water in the tank will rise by 7 cm. So we have a pipe through which the water is flowing and from there it goes into a rectangular tank. So we have to find the time in which the level of the water in the tank will rise by 7 cm. So first of all let's recall the formula for the volume of a cylinder. This is equal to pi r square h, r is the radius of the base of the cylinder, h is the height of the cylinder. This is the key idea to be used in this question. Now let's see the solution. Now that we need to find the time in which the level of water in the tank will rise by 7 cm. So first of all we suppose let the time in which the level of water in the tank rises by 7 cm be equal to x r's. Now we are also given the rate at which the water is flowing is given as 5 km per hour. So therefore we say the length of the water column in x r's would be given by x into 5 or 5 into x km. Since the rate at which the water is flowing is 5 km per hour. So the length of the water column in x r's is 5 into x km. Let's convert this into meters by multiplying it by 1000. So this is equal to 5000 x m. Now clearly we have that the water column forms a cylinder. Now the length of the water column in x r's that is 5000 x m is the height of the cylinder. So the height of the cylinder given by capital H is equal to 5000 x m and we are also given the radius of the cylinder as capital R is equal to diameter of the pipe that is 14 cm upon 2. So capital R is equal to 14 upon 2 equal to 7 cm. Let's convert this into meters. So this is equal to 7 upon 100 meters. Then we have volume of the water flowing through the cylindrical pipe in x r's is equal to pi r square into h. Let's substitute the values for r and h. So this is equal to pi into 7 upon 100 whole square into 5000 x meter cube is the volume of water flowing through the cylindrical pipe in x r's. Now putting the value of pi r's 22 upon 7 this into 7 upon 100 into 7 upon 100 into 5000 x. Now these two 0 cancels with these two 0 then 50 2 times is 100 and 2 11 times is 22. This 7 cancels with this 7 and so this is equal to 11 into 7 that is 77 x meter cube is the volume of water flowing through the cylindrical pipe in x r's. As in the question we have that the water through the pipe goes into a rectangular tank whose dimensions are given to us then the volume of water that falls into the tank in x r's is equal to 50 into 44 which is the area of the rectangular tank into 7 upon 100 which is the radius of the cylinder that would be the height of the tank. So this meter cube would be the volume of water that falls into the tank in x r's. Now 52 times is 100 and 2 22 times is 44 so this is equal to 154 meter cube. Now the volume of the water flowing through the cylindrical pipe in x r's is equal to the volume of water that falls into the tank in x r's. So this is equal to 77 x which is the volume of water flowing through the cylindrical pipe in x r's is equal to 154 that is the volume of water that falls into the tank in x r's. So from here we can find out the value of x is equal to 154 upon 77 77 2 times is 154 so we get x is equal to 2 and we had assumed that the time in which the level of water in the tank rises by 7 centimeters to be x r's so we can now say level of water in the tank rises by 7 centimeters in 2 r's. So 2 r's is our final answer. This completes the session. Hope you have understood the solution of this question.