The Travel:

You have secured a foreign exchange semester with the Arctic University of Norway $($UiT$)$ at their campus in Troms$.$ The City of Troms$$ has more than $75,000$ inhabitants, the university more than $11,000$ students, and all of this lies more than $200$ miles north of the arctic circle. While you are dreaming of Northern Lights and midnight sun, your S&T roommates are just as excited, which however maybe because they will now have your part of the apartment as an open space for partying with friends. They decide to throw you a farewell party with your favorite food from Burger King, which they expect you will dearly miss at UiT. To enhance the atmosphere $($in this sentence, atmosphere is not used as the unit of pressure$),$ you suggest filling helium balloons from a small $1\mathrm{.}00$ L compressed$-$helium gas cylinder. Will your gas cylinder that is pressurized to $200$ atm give you enough helium to fill $10$ perfectly round Latex Crystal$-$tone Color Balloons $($diameter of $30\mathrm{.}0$ cm$),$ which completely inflate at a pressure of $1\mathrm{.}2$ atm?

Useful information:

$($a$)$ Room temperature is $25\backslash$deg C

$($b$)$ Helium may be considered ideal only at low pressures $(<5$ atm$).$

$($c$)$ It is relatively easy to solve the Van der Waals equation for pressure; solving it for volume or number of moles leads to cubic equations.

$($d$)$ Van der Waals constants for He: a $=0\mathrm{.}03502$ L$2$ atm mol$-2,$ b $=0\mathrm{.}0237$ L mol$-1$