I got a problem which I am pondering about for a while.

It's about a general relationship between volume and surface area. It could also be between a line and an area.

The thing is that it's possible that two objects can have the same volume but different surface area. I don't understand that logically. It's completely clear and fine for me in a mathematical way, but not in a logical way.

Let's consider an object with the volume x. Now this volume is enclosed, covered, trapped (whatever you want to call it) by a surface area. I can change the shape of the volume, and still the surface would enclose this volume - but the surface area can change during this.

The same with a plane. The plane is encompassed by lines. There are many shapes of the plane, it's still got the same area. But why would the lenght of the lines (circumference) change when just the shape changes, but not the area.

I mean, it's technically still the same area, just in another shape - or the same volume, just in another shape.

Now my question to solve this problem would be:

Is there a general relationship, applicable to all shapes of volumes and surfaces, which "links" volume and surface area (or circumference and area)?

Is there a concept which can be used to consider such things as volume and area in a way that my problem wouldn't exist?

Thanks in advance.