Answer
$2000\ mL$ or $2\ L$. This is possible because the volume of such containers us less than $5\ L$ but a lot of blood would have to be removed for the nanocontainers to fit, the body uses blood to transport oxygen from the lungs. If the nanoconatiners could be refilled at the lungs as or more efficiently than red blood cells, this would be a plausible procedure.
Work Step by Step
Each nanocontainer has a volume of $1×10^{−21}\ cm3$ which is the same as $1×10^{−21}\ mL$. So $2.0×10^{24}\ nanocontainers$ would occupy a volume of $2.0×10^{24}\times 1×10^{−21}\ mL=2000\ mL$.
