 Hello and welcome to the session. The given question says, a solid metallic sphere of diameter 21 cm is melted and recasted into a number of small cones, each of diameter 7 cm and height 3 cm. Find the number of cones so formed. Suppose this is a solid metallic sphere of diameter 21 cm, it is melted and recasted into a number of small cones. We have to find the number of cones. We are given here that the diameter of these cones is 7 cm and height of each cone is 3 cm. So, let n be the number of cones so formed. Then the volume of this metallic sphere must be equal to n into the volume of each small cone. Let us denote it by a small v. So, by this relation we shall be finding the value of n that is the number of cones. Let us move on to the solution. First we shall find the volume of the metallic sphere. We are given that diameter of the sphere is equal to 21 cm therefore radius of sphere which is equal to 21 on 2 cm. And let us denote the radius of this sphere by small r. Therefore, its volume which we have denoted by capital V is given by 4 divided by 3 by r whole cube. Substituting the value of r we have 4 divided by 3 into pi into 21 divided by 2 whole cubes into cm cube. So, this is the volume of this sphere. Let us denote this by equation number 1. Also we are given that diameter of the cone which is formed from solid metallic sphere is equal to 7 cm therefore radius of cone is equal to 7 divided by 2 cm and let us denote it by r1. Also we are given the height of the cone which is equal to 3 cm. Therefore volume of cone denoting it by small v is equal to 1 divided by 3 pi r1 square into h where h is the height of the cone. And on substituting the values we have 1 divided by 3 into pi r1 as 7 divided by 2 cm. Therefore r1 square is 7 divided by 2 whole square into h is 3 into cm cube. Let us be equation number 2. Now we have to find the number of cones formed from this solid metallic sphere. Let the number of cones formed is equal to n. Then by this relation we have the volume of solid metallic sphere which is capital V equal to n into small v where small v is the volume of each smaller cone. Therefore we have n is equal to capital V divided by small v. On substituting the value in the numerator we have 4 divided by 3 into pi into 21 divided by 2 whole cube into cm cube. And in the denominator we have 1 divided by 3 into pi into 7 divided by 2 whole square into 3 into cm cube. And this is from 1 and 2 and on simplifying this we get 126. Therefore n is equal to 126. Hence our answer is number of cones which are formed when a solid metallic sphere of diameter 21 cm is melted and recast it is equal to 126. So this completes the session. Bye and take care.