If two different shapes have the same volume, does that mean they have the same surface area?
You can easily find a counterexample.
Consider a cube of, say, 1 unit length and find it's volume and surface areas.
Then consider a cuboid with sides 2, 1 and 0.5 units long (which has the same volume as the unit cube) and find it's surface area.
You should find that the surfaces areas are different, which dis-proves your statement.