Question

Why surface area and curved surface area is changed during the conversion of one shape to another and volume is not changed.

Answer 1

That can be explained with a small example.
imagine you have a small lump of clay with a volume of x m^3 as volume.
First we make it into a sphere. It's SA is given by 4πr^2 and volume is given by 4/3πr^3.
Then we change the shape of the clay into a cylinder its SA is given by πr(r+h) and volume by π(r^2)h.
Now take a step back and observe, while we change the shape of the clay from a sphere to a cylinder we did not add any more clay nor we removed any. So their volume should be the same as volume is the same occupied by an object.
But SA being the area which is in contact with the air or surrounding it surely must have changed.
​​​​​​This is true for every other shape. If the amount of substance needed to make it doesn't change then their volume remains constant.
This can also be understood by tearing the first sphere into half. Their added volume of the 2 hemisphere are same
4/3πr^3=1/2(4/3πr^3)+1/2
(4/3πr^3)
But the surface area is not the same because now there is an added area of the splitted part. So the SA has increased but the volume remains the same.
Just remember surface area is the area of the part in contact with air or the surrounding it will change with change on shape.