 Hello and welcome to the session. Let us discuss the following question which says a container shaped like a right circular cylinder having diameter 12 centimeter and height 15 centimeter is full of ice cream. This ice cream is to be filled into cones of height 12 centimeter and diameter 6 centimeter having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream. Before moving on to the solution let's recall few formulas that is volume of a cylinder is given by pi r square h where r is the radius and h is the height of the cylinder. Volume of cone is given by 1 upon 3 pi r square h where r is the radius and h is the height of the cone. And volume of a hemisphere is given by 2 upon 3 pi r cube where r is the radius of the hemisphere. This is the key idea for this question. Now let's move on to its solution. Here we have a container which is in the shape of a right circular cylinder whose diameter is 12 centimeters and height is 15 centimeters and this is full of ice cream. So first of all let's find out the volume of ice cream in this container. So for this we will find out the volume of this right circular cylinder. Thus for container diameter is given to be 12 centimeters so this implies radius of the container say r will be equal to 12 upon 2 centimeters that is 6 centimeters and the height say h of the container is given to be 15 centimeters. So the volume of container will be given by pi r square h. Now let's substitute the values so we get pi into r square that is 6 square into h that is 15 centimeter cube which will be equal to 540 pi centimeter cube. Now the ice cream in this container has to be filled into ice cream cones which is in the shape of a cone with a hemispherical top. So that means the volume of ice cream in an ice cream cone will be equal to volume of this cone plus volume of hemispherical top. Thus we have volume of an ice cream cone is equal to volume of cone plus volume of hemisphere. So first of all consider the cone for this cone we are given that the diameter is equal to 6 centimeters so its radius say r will be equal to 6 upon 2 centimeters that is 3 centimeters and the height of the cone say h is given to be 12 centimeters. So now the volume of cone will be equal to 1 by 3 pi r square h on substituting the values we will get 1 by 3 into pi into r square that is 3 square into h that is 12 centimeter cube and this will be equal to 36 pi centimeter cube. Now we will find the volume of this hemispherical top so consider the hemisphere here the diameter of the hemisphere will be same as the diameter of the cone. So for the hemisphere diameter is equal to 6 centimeters so this implies that the radius say r1 of hemisphere will be equal to 6 upon 2 centimeters that is 3 centimeters. So let us find the volume of hemisphere which is given by 2 by 3 pi r1 cube substituting the values we get 2 by 3 into pi into r1 cube that is 3 cube centimeter cube which will be equal to 18 pi centimeter cube. So now we got the volume of cone and the hemisphere therefore volume of an ice cream cone will be equal to volume of cone that is 36 pi centimeter cube plus volume of hemisphere that is 18 pi centimeter cube so this will be equal to 54 pi centimeter cube. So here the volume of an ice cream cone is 54 pi centimeter cube and the volume of the container is 540 pi centimeter cube. Now we know that volume of container will be equal to volume of one ice cream cone into number of cones. So this implies volume of container that is 540 pi will be equal to volume of one ice cream cone that is 54 pi into number of cones. From here we get that number of cones will be equal to 540 pi upon 54 pi which will be equal to 10. So 10 cones can be filled with the ice cream and thus this is the required answer to this question. With this we finish this session. Hope you must have understood the question. Goodbye take care and have a nice day.