 Hello and welcome to the session. In this session we discuss the following question which says a cylindrical bucket 14 cm in radius and 28 cm high is full of water. The water is emptied into a rectangular tank 22 cm long and 16 cm wide find the height of the water level in the tank. First let's recall the formula for the volume of a cylinder this is equal to pi r square h cubic units where this h is the height of the cylinder r is the radius of the base of the cylinder and the volume of a cuboid is equal to n into b into h cubic units n is the length of the cuboid b is the depth of the cuboid and h is the height of the cuboid. This is the key idea to be used in this question. Now we move on to the solution. Now the radius of the cylinder is 14 cm so we have the radius of cylinder r be equal to 14 cm then the height of the cylinder is 28 cm that is we are given h as 28 cm so the volume of cylindrical bucket or the cylinder say v1 is equal to pi r square that is 14 square into h that is 28 cm 2. Next it's given to us that the length of the rectangular tank that is l is equal to 22 cm and it's also given that the breadth of the rectangular tank that is b is equal to 16 cm. We take let the height of the rectangular tank be at centimeters. So now the volume of the water in the rectangular tank is equal to l into b into h centimeter cube since the rectangular tank is cuboidal in shape so this is equal to 22 into 16 into h centimeter cube. Now in the question we are given that the water in the cylindrical bucket is emptied into the rectangular tank so obviously the volume of the cylinder would be equal to the volume of water in rectangular tank. Now we already have the volume of cylinder as pi 14 square into 28 centimeters cube that is pi into 14 square into 28 is equal to the volume of the water in the rectangular tank which is 22 into 16 into h centimeter cube that is this further gives us 22 upon 7 into 14 into 14 into 28 is equal to 22 into 16 into h and from where we get h is equal to 22 into 14 into 14 into 28 upon 7 into 22 into 16. Now this 22 and 22 gets cancelled 7 2 times is 14, 2 8 times is 16, 2 4 times is 8 and 2 7 times is 14 then 4 7 times is 28 so this is equal to 7 into 7 and we get h is equal to 49 centimeters that is the height of the rectangular tank is 49 centimeters or we can say height of the water level in the tank is equal to 49 centimeters so this is the required answer this completes the session hope you have understood the solution for this question.