 Hello and welcome to the session I am Deepika here. Let's discuss the question which says a vessel is in the form of an inverted cone. Its height is 8 cm and radius of its top which is open is 5 cm. It is filled with water up to the brim when red shorts each of which is a sphere of radius 0.5 cm are dropped into the vessel one fourth of the water flows out. Let's find the number of red shorts dropped in the vessel. Let us first recall the formulas for volume of a cone and volume of a sphere. Volume of a cone is equal to 1 by 3 pi r square h where r is the radius and h is the height of the cone and volume of a sphere is equal to 4 by 3 pi r cube where r is the radius of the sphere. So this is a key idea behind that question. We will take the help of these formulas to solve the above question. So let's start the solution. A vessel is in the form of an inverted cone and it is filled with water up to the brim. Then the radius of the cone it is given r1 is equal to 5 cm and height of the cone is equal to 8 cm. Now the cone is filled with water therefore the volume of water in the cone is equal to now according to our key idea volume of cone is 1 by 3 into pi into radius square into h. So this is equal to 1 by 3 pi r1 square into h and this is again equal to 1 by 3 into pi into 5 square that is 5 into 5 into 8 cm cube. When the led shots are dropped into the vessel one fourth of the water flows out. Now the volume of water displaced by the led shot is equal to 1 by 4 of volume of water in the cone. So this is equal to 1 by 4 into 1 by 3 into pi into 5 into 5 into 8 cm cube. Let r2 is the radius of the led shot therefore r2 is equal to 0.5 cm it is given. Now the volume of led shot is equal to now led shot is in the form of a sphere. Now according to our key idea the volume of sphere is 4 by 3 pi r cube. Now r is here 0.5 cm so we have the volume of a led shot is equal to 4 by 3 into pi into r2 cube and this is equal to 4 by 3 into pi into 0.5 cube. Now we want to find the number of led shots dropped in the vessel. So to find the number of led shot dropped in the vessel we will divide the volume of water displaced by the led shots with the volume of a led shot. Therefore the number of led shots is equal to volume of water displaced by the led shots upon volume of a led shot. Now this is equal to 1 by 4 into 1 by 3 pi r square inch pi into 5 into 5 into 8 cm cube divided by 4 by 3 pi into 0.5 into 0.5 into 0.5 cm cube and this is again equal to 1 by 4 into 1 by 3 pi into 5 into 5 into 8 into 3 by 4 pi into 10 upon 5 into 10 upon 5 into 10 upon 5 and this is equal to on cancellation we have into 2 into 10 and this is equal to 100. Hence the answer for the above question is that number of led shots dropped in the vessel is 100. I hope the solution is clear to you, buy and check here.