Step 1: Volume of the spherical balloon, $R = 20$ cm :
$$V_1 = \frac{4}{3}\pi R^3 = \frac{4}{3} \times \frac{22}{7} \times (20)^3 = \frac{4}{3} \times \frac{22}{7} \times 8000$$
Step 2: Volume of one thermocol ball, $r = 0{\cdot}5 = \dfrac{1}{2}$ cm :
$$v = \frac{4}{3}\pi r^3 = \frac{4}{3}\pi \times \frac{1}{8} = \frac{\pi}{6}$$
Step 3: Volume of $1000$ balls :
$$V_2 = 1000 \times \frac{\pi}{6} = \frac{1000\pi}{6} = \frac{500\pi}{3}$$
Step 4: Volume of air $= V_1 - V_2$
$$= \frac{32000\pi}{3} - \frac{500\pi}{3} = \frac{31500\pi}{3} = 10500\pi$$
Step 5: $$= 10500 \times \frac{22}{7} = 33000$$
Hence the volume of air in the balloon $= 33000\ \text{cm}^3$.