Ahollow steel ball weighs 1 kilogram. what must its volume be for it to float in water

Well first of all, nothing "weighs" a kilogram.  "Kilogram" is a unit of mass,
not force, and the weight of 1 kilogram of mass depends on where it is ...
about 2.2 pounds on Earth, about 5.8 ounces on the Moon, about 11.8
ounces on Mars, etc.

But to answer this question, we don't even need to talk about weight.
We only need to find the density of the ball.  We know that if it's more
than the density of water, then the ball will sink, and if its less than the
density of water, then the ball will float.

-- The density of water is  1.00 gram/cm³ .

-- The density of the ball must be  1.00 gram/cm³ or less, to float.
 
                                    Density = (mass) / (volume)

                                    1 gram/cm³  =  (1000 grams) / (volume)

Multiply each side by (volume):    (Volume) x (1 gm/cm³) = (1,000 gm)

Divide each side by 1gm/cm³ :      Volume = (1000 gm) / (1 gm/cm³)

                                                                  = 1,000 cm³  =  1 liter

No it doesnt because it can be any number.