 Hello, and welcome to the session. I am Deepika and I am going to help you to solve the following question the question says Our sphere of diameter 12 centimeter is dropped in a right circular cylindrical vessel Partly filled with water. If the sphere is completely submerged in water, the water level in the cylindrical vessel rises by 3 and 5 by 9 centimeter find the diameter of the cylindrical vessel Now we know that the volume of Sphere is equal to 4 over 3 pi rq where r is the radius of the sphere and Volume of cylinders is equal to pi r square h Where r is the radius of the base of this cylinder and h is the height of the cylinder So this is a key idea behind our question We will take the help of this key idea to solve the above question So, let's start the solution Now according to the given question a sphere of diameter 12 centimeter is dropped in a right circular cylindrical vessel Which is partly filled with water So first of all, we will find the volume of sphere which is dropped in a right circular cylindrical vessel Now we are given the diameter of the sphere is equal to 12 centimeter therefore the radius of The sphere is equal to 6 centimeter As we know radius is half of diameter. So if diameter is 12 centimeter then radius is 6 centimeter So according to our key idea the volume of the sphere Which is dropped in a cylindrical vessel is equal to 4 over 3 Into pi Into rq now r is here 6 centimeter So the volume of the sphere is equal to 4 over 3 into pi into 6 into 6 into 6 centimeter q and This is again equal to 280 a pi centimeter q Now again according to the given question if the sphere is completely submerged in water the water level in the cylindrical vessel rises by 3 and a 5 by 9 centimeter So this is the height of the water level raised in the cylindrical vessel and this is equal to 3 and a 5 by 9 centimeter, which is again equal to 32 over 9 centimeter Now we have to find the diameter of the cylindrical vessel so let R be the radius of the cylindrical vessel therefore the volume of water raised in cylindrical vessel is given by pi r-spirits Where h is the height of water level raised in cylindrical vessel, which is given to us 32 over 9 centimeter So the volume of water raised in cylindrical vessel is equal to pi into r square into 32 over 9 centimeter q and This is equal to 32 over 9 pi r square centimeter q now the volume of water raised in cylindrical vessel is equal to the volume of the sphere Which is dropped in the cylindrical vessel Now we have the volume of the sphere is equal to 288 by centimeter q And the volume of water raised in cylindrical vessel is equal to 32 over 9 pi r square centimeter q so this implies 32 over 9 pi r square centimeter q is equal to 288 by centimeter q This implies r square is equal to 288 into 9 over 32 centimeter square Again this implies r square is equal to 9 into 9 centimeter square and this implies r is equal to 9 centimeter Hence the diameter of the cylindrical vessel is equal to 18 centimeter. So 18 centimeter is the answer for the question This completes our session. I hope the solution is clear to you by and have a nice thing