1. A solid surrounded by a gas experiences a force of buoyancy(?) which has the opposite direction of the weight of the solid and has the absolute value of the weight of the displaced gas. (Principle of Archimedes)

2. Since the body looses all it's weight you get as force of buoyancy $\displaystyle F_b = 1 kg \cdot 9.81 \frac{m}{s^2} = 9.81 N$

3. The densitiy of the surrounding air is $\displaystyle d_a = 1.29 \frac{kg}{m^3}$

The force of buoyancy is calculated by: $\displaystyle F_b = V_{air} \cdot d_a \cdot 9.81 \frac{m}{s^2}$

4. Solve for $\displaystyle V_{air}$ which must be as large as the volume of the Helium gas.