 Hi and welcome to the session. Let us discuss the following question. Question says, matric spheres of radii, 6 cm, 8 cm and 10 cm respectively are melted to form a single solid sphere. Find the radius of the resulting sphere. First of all, let us understand that volume of sphere is equal to 4 upon 3 pi r cube where r is the radius of the sphere. Now we will use this formula as our key idea to solve the given question. Let us now start with the solution. Now first of all let us assume that r be the radius of the resulting sphere. So we can write let r be the radius of the resulting sphere. We have given that three spheres form a single sphere. Now this implies volume of three spheres is equal to volume of a single resulting sphere. Now let us assume that radii of three spheres are r1, r2 and r3. We have given that radii of three spheres are 6 cm, 8 cm and 10 cm. So we can write r1 is equal to 6 cm, r2 is equal to 8 cm and r3 is equal to 10 cm. Now according to the question volume of three spheres is equal to volume of the resulting sphere. So we can write volume of three spheres is equal to volume of single resulting sphere. Now we know volume of the sphere is equal to 4 upon 3 pi r cube where r is the radius of the sphere. Now volume of the three spheres is equal to 4 upon 3 pi r1 cube plus 4 upon 3 pi r2 cube plus 4 upon 3 pi r3 cube. Now we will find volume of single sphere. We know radius of the single sphere is r. So its volume is equal to 4 upon 3 pi r cube. Now this further implies 4 upon 3 pi multiplied by r1 cube plus r2 cube plus r3 cube is equal to 4 upon 3 pi multiplied by r cube. Clearly we can see 4 upon 3 pi is common in all these three terms. Now dividing both the sides of this expression by 4 upon 3 pi we get r1 cube plus r2 cube plus r3 cube is equal to r cube. Now substituting corresponding values of r1, r2 and r3 in this expression we get 6 cube plus 8 cube plus 10 cube is equal to r cube. Now 6 cube is equal to 216, 8 cube is equal to 512 and 10 cube is equal to 1000. So we get 216 plus 512 plus 1000 is equal to r cube. Now adding these three terms we get 1728 is equal to r cube. Now this can be further written as 12 cube is equal to r cube. We know 1728 is equal to 12 cube. Now taking cube root on both the sides we get 12 is equal to r or we can simply write it as r is equal to 12 centimeters. Now we get radius of the resulting sphere is equal to 12 centimeters. This is our required answer. This completes the session. Hope you understood the solution. Take care and have a nice day.