 Hi, and how are you all today? Hi, and how are you all today? The question says the internal and external radii of a circle of a hollow spare are 3 cm and 5 cm respectively. The spare is melted to form a solid cylinder of height 2, 2 by 3 cm, find the diameter and curved surface area of the cylinder. So here, first of all, let the internal radii of the spare R be equal to 3 cm. Therefore, the external radii of the spare let it be capital R be equal to 5 cm. Let the radius of the cylinder, let us take it as x be equal to, let it be equal to x cm. Also, we are given the height of the cylinder as 2, 2 by 3 cm that is equal to 8 by 3 cm. Now, firstly, we are given that the volume of the hollow spare is equal to the volume of the cylinder. So, volume of the hollow spare is 4 by 3 by capital R cube minus small r cube and that is equal to the volume of the cylinder that is pi r square h pi r is x to x square h that is 8 by 3. First of all, let us find out the value of x. The next step is to substitute the known values 4 by 3 pi and pi will get cancelled. 5 cube minus 3 cube is equal to x square into 8 by 3, further equal to 4 by 3 125 minus 27 is equal to r square into 8 by 3. Further, we have 4 by 3 into 98 equal to r square into 8 by 3. Which is 4 by 3 into 98 into 3 by 8 equal to x square. Now, let us simplify it first. So, we have, so under root 49 will be equal to x that is further 7 cm is equal to rx which is the radius of the cylinder. Now, first of all we were required to find out the diameter of the cylinder that will be equal to 2 into r that is equal to 2 into 7 further 14 cm. And we are required also to find out the curved surface area of the cylinder. It is equal to 2 pi that is 8 pi 3 44 into 8 by 3 and that is equal to 117.33 cm square cm square. So, these two are the required answer to the given question. So, this completes the solution. Hope you understood it well. Have a nice day.