 Hello and welcome to the session. In this session we discussed the following question which says, a sphere of diameter 6 cm is dropped in a right circular cylindrical vessel partly filled with water. The diameter of the cylindrical vessel is 12 cm. If the sphere is completely submerged in water, by how much will the level of water rise in the cylindrical vessel? So we are given a cylindrical vessel and a sphere which is dropped in the cylindrical vessel that is partly filled with water. So the sphere is completely submerged in water and so we have to find out by how much will the level of water rise in the cylindrical vessel. For this we should know the volume of a sphere which is equal to 4 by 3 pi r cube. r is the radius of the sphere. Then volume of a cylinder is equal to pi r square h. r is the radius of the base of the cylinder and h is the height of the cylinder. So this is the key idea for this question. Now let's see its solution. We are given the diameter of the sphere as 6 cm. Obviously its radius given by r is equal to 6 upon 2 that is equal to 3 cm. Now we can find out the volume of the sphere given by v is equal to 4 by 3 pi r cube putting the value of this r. So this is equal to 4 by 3 pi into 3 cube cm cube or you can say this is equal to 36 pi cm cube is the volume of the sphere. Then again we have a cylindrical vessel with diameter 12 cm. So the radius of the cylinder given by r dash is equal to 12 upon 2 equal to 6 cm is the radius of the cylindrical vessel. Let the height of the cylinder be equal to x cm. In the question we have that the right circular cylindrical vessel is partly filled with water. So when we would drop the sphere in the cylindrical vessel the level of water would rise. So the volume of the water displaced by the sphere would be equal to the volume of the sphere. Now we have the radius of the cylinder and the height of the cylinder as x cm. So the volume of the cylinder given by v dash would be equal to pi r dash square into h that is equal to pi into 6 square into h cm cube or you can say this is equal to 36 pi into h cm cube is the volume of the cylinder. Or you can say this is same as the volume of water displaced by the sphere and this is equal to the volume of the sphere. So you have 36 h into pi is equal to the volume of the sphere which is 36 pi. So from here we have h is equal to 36 pi upon 36 pi so this is equal to 1 that is we have h is equal to 1 cm. As we say the water level rises by 1 cm. So this is the final answer. This completes the session. Hope you have understood the solution of this question.