#### Answer

He wants the balloon to lift 20 kg, or to have a buoyant force of (20 kg)(g) = 200 N. The buoyant force is the weight of the displaced air, so 200 N = (balloon volume)(weight density of air). On page 271, the latter number is given as $12 \frac{N}{m^{3}}$.
Solve for the volume of the balloon, $\frac{200 N}{12 N/m^{3}} = 17 m^{3}$.
Note: for this calculation to work out with the numbers provided in the question, the mass of the helium should be neglected. Helium has a mass density of 0.1786 $\frac{kg}{m^3}$, and if the helium is taken into account, a balloon volume of about $20 m^{3}$ would be required.

#### Work Step by Step

This is discussed on page 271.