 Hi and welcome to the session. Let us discuss the following question. Question says, a maplix sphere of radius 4.2 centimeters is melted and recast into the shape of a cylinder of radius 6 centimeters. Find the height of the cylinder. 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 and volume of cylinder is equal to pi r square h where r is the radius of the cylinder and h is the height of the cylinder. Now we will use these formulas as our key idea to solve the given question. Let us now start with the solution. Now we are given that radius of sphere that is r1 is equal to 4.2 centimeters. Radius of cylinder that is r2 is equal to 6 centimeters. We have to find height of the cylinder that is we have to find h. Now we are given that sphere is recast into a cylinder. This implies volume of sphere is equal to volume of cylinder. From key idea we know volume of sphere is equal to 4 upon 3 pi r cube and here radius of sphere is r1 so we can write volume of given sphere is equal to 4 upon 3 pi multiplied by cube of r1 and volume of cylinder from key idea we know is equal to pi r square h. Now in this formula we will substitute r2 for r to get volume of this given cylinder. Now we can write volume of sphere is equal to 4 upon 3 pi multiplied by cube of r1 is equal to pi multiplied by square of r2 multiplied by h. Now substituting corresponding values of r1 and r2 in this expression we get 4 upon 3 pi multiplied by cube of 4.2 is equal to pi multiplied by square of 6 multiplied by h. Dividing both the sides of this expression by pi we get 4 upon 3 multiplied by cube of 4.2 is equal to 36 multiplied by h we know square of 6 is equal to 36. Now dividing both the sides of this expression by 36 we get 4 upon 3 multiplied by 4.2 multiplied by 4.2 multiplied by 4.2 upon 36 is equal to h. Now we will simplify this expression we know 4 multiplied by 9 is equal to 36 and 3 multiplied by 1.4 is equal to 4.2. Similarly we know 3 multiplied by 3 is equal to 9 and 3 multiplied by 1.4 is equal to 4.2. Here also 3 multiplied by 1.4 is equal to 4.2. Now multiplying these three terms we get 2.744 is equal to h or we can simply write it as h is equal to 2.744 centimeters. We know h is the height of the cylinder so we get height of cylinder is equal to 2.74 centimeters. Now this is our required answer. This completes the session. Hope you understood the solution. Take care and keep smiling.