Volume of one balloon which is to be filled
$= \large\frac{4}{3}\pi (\large\frac{21}{2})^3$
= 4851 mL
= 4.851 litre
Let n balloon are filled , then volume of $H_2$ occupied by balloons = $4851\times n $
Also cylinder will not be empty and it will occupy volume of
$H_2 $= 2.82 litre
$\therefore$ Total volume occupied by $H_2$ at NTP = $4.851\times n + 2.82 litre$
$\therefore$ at STP
$P_1 = 1 atm$
$V_1 = 4.851\times n + 2.82$
$T_1 = 273 K$
Available $H_2$
$P_2 = 200\;atm$
$T_2 = 300K$
$V_2 = 2.82\;litre$
$\therefore \large\frac{P_1V_1}{T_1} = \large\frac{P_2V_2}{T_2}$
$\large\frac{1\times(4.851n + 2.82)}{273} = \large\frac{20\times2.82}{300}$
$\Rightarrow n = 10$
Hence answer is (B)