– The radius of the balloon $r = 0.35text{ m}$

– The pressure of the balloon $P = 3.1 cdot 10^{5}text{ Pa}$

– The temperature of the balloon $T = 22text{textdegree}text{C} = 295.15text{ K}$

To calculate the number of helium atoms in the balloon we use the Ideal Gas Equation:

$$
begin{equation*}
PV = N , k , T
end{equation*}
$$

rearranging for number of particles:

$$
begin{equation*}
N = frac{pV}{k , T}
end{equation*}
$$

Where the volume of the spherical balloon is $V = frac{4}{3} , r^3 , pi$

Plugging in the values we get:

$$
begin{align*}
N = frac{2.1 cdot 10^{5}text{ Pa} cdot frac{4}{3} , cdot left(0.35text{ m} right)^3 cdot pi }{1.38 cdot 10^{-23} , frac{text{J}}{text{K}} cdot 295.15text{ K}} = 136.62 cdot 10^{23} = 1.37 cdot 10^{25}
end{align*}
$$

– The number of moles of air in the tire $n = 1.5text{ mol}$

– The gauge pressure in the tire $P = 245text{ kPa}$

– The temperature of the tire $T = 282text{ K}$

To calculate the volume of tire we use the Ideal Gas Equation:

$$
begin{equation*}
PV = n , R , T
end{equation*}
$$

rearranging for volume:

$$
begin{equation*}
V = frac{n , R , T}{P}
end{equation*}
$$

Where the pressure in the tire is the sum of the gauge pressure and atmospheric pressure $P = P_{text{gauge}} + P_{text{atmosphere}}$

Plugging in the values we get:

$$
begin{align*}
V = frac{1.5text{ mol} cdot 8.31 , frac{text{J}}{text{mol K}} cdot 282text{ K} }{(245text{ kPa} + 101text{ kPa}) } = 0.01016text{ m}^3 approx 1.02 cdot 10^{-2}text{ m}^3
end{align*}
$$