 Hi and welcome to the session. Let us discuss the following question. A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream. First of all let us understand that volume of cylinder is equal to pi r square h where r and h are the radius and height of the cylinder. Volume of cone is equal to 1 upon 3 pi r square h where r and h are the radius and height of the cone and volume of hemisphere is equal to 2 upon 3 pi r cube where r is the radius of the hemisphere. This is the key idea to solve the given question. Let us now start with the solution. We are given a container shaped like a right circular cylinder having diameter 12 cm and height 15 cm and this container is full of ice cream. First of all let us find out volume of ice cream in this cylindrical container. Now we know diameter of the cylindrical container is equal to 12 cm. This implies radius that is r is equal to 12 upon 2 cm that is 6 cm. We know radius is half of diameter. We are also given that height of cylindrical container is equal to 15 cm. So we can write height of cylinder that is h is equal to 15 cm. From key idea we know volume of cylinder is equal to pi r square h where r and h are radius and height of the cylinder. Now substituting corresponding values of r and h in this formula we get pi multiplied by square of 6 multiplied by 15 cm cube. Now solving it further we get 540 pi cm cube. Now we know volume of cylinder is equal to volume of ice cream in this cylinder. So we can write volume of ice cream in the cylindrical container is equal to 540 pi cm cube. Now ice cream in this cylindrical container is to be filled into cones of height 12 cm and diameter 6 cm having a hemispherical shape on the top. Now let us find out volume of ice cream in the cone. Now clearly we can see volume of ice cream in the cone is equal to volume of this cone plus volume of this hemisphere. Now we are given that diameter of the cone is equal to 6 cm. This implies radius of the cone that is r is equal to 6 upon 2 cm that is 3 cm. We know radius is equal to half of diameter. Height of the cone that is h is equal to 12 cm. From key idea we know volume of cone is equal to 1 upon 3 pi r square h where r and h are the radius and height of the cone. Now substituting corresponding values of r and h in this formula we get 1 upon 3 multiplied by pi multiplied by square of 3 multiplied by 12 cm cube. Now this can be further written as 1 upon 3 pi multiplied by 3 multiplied by 3 multiplied by 12 cm cube 3 and 3 will get cancelled and we get volume of cone is equal to 36 pi cm cube. So volume of this cone is equal to 36 pi cm cube. Now let us find out volume of this hemispherical part. Now we are given that radius of hemisphere is equal to radius of this cone and we know radius of this cone is equal to 3 cm. So radius of hemisphere that is r1 is equal to 3 cm. Now we know volume of hemisphere is equal to 2 upon 3 pi r cube where r is the radius of the hemisphere. So volume of given hemisphere is equal to 2 upon 3 pi multiplied by r1 cube. Now substituting corresponding value of r1 in this formula we get 2 upon 3 pi multiplied by cube of 3 cm cube. Now simplifying it further we get 18 pi cm cube. Now we know total volume of the ice cream in the cone is equal to volume of cone plus volume of hemisphere. So we can write total volume of ice cream in a cone is equal to volume of cone plus volume of hemisphere. Now we know volume of cone is equal to 36 pi. So we get total volume of ice cream in a cone is equal to 36 pi plus and volume of hemisphere is equal to 18 pi 18 pi plus 36 pi cm cube is equal to total volume of ice cream in a cone. Now adding these two terms we get 54 pi cm cube. Now we get total volume of ice cream in a cone is equal to 54 pi cm cube. Now we have to find the number of such cones which can be filled with ice cream. Now let us assume that number of cones is n. So we can write let the number of cones be n. Now we know total number of cones multiplied by volume of ice cream in one cone is equal to total volume of ice cream. So we can write n multiplied by 54 pi is equal to 540 pi. We know total volume of ice cream is equal to volume of the cylindrical container and volume of the cylindrical container is equal to 540 pi cm cube. Now dividing both the sides of this equation by 54 pi we get n is equal to 540 pi upon 54 pi. Now pi and pi will get cancelled and we will cancel common factor 54 from numerator and denominator both and we get required number of cones is equal to 10. So our required answer is number of cones that can be filled with ice cream is equal to 10. This completes the equation. Hope you understood the solution. Take care and keep smiling.