Is it possible to find an example of a bounded region in the x, y plane that satisfies the following condition : when you revolve the region about the x axis you obtain a solid that has a volume equals its surface area

Answer 1

volume is in length^3 units, surface area is in lenght^2 units.

So no, it is not possible to equate those. Area cannot be equal to volume.

45cm^2=? 45cm^3
1=?cm No, cm cannot be unitless

Now, I assume your teacher is not considering units...just asking if the numerals can equal.

Yes, if one does not care about units, they can be "equaled", whatever that means.

It really is a stupid question, perhaps your teacher was not thinking.

Answer 2

yes he does not care about the unit he just want the value using integration