Question

$\mathrm{p}=20+4\times \frac{\frac{4}{40}}{{10}^{-2}}=50$

$\mathrm{mg}+\frac{4}{3}{\mathrm{\pi r}}^3{\mathrm{\rho }}_{\mathrm{He}}\mathrm{g}=\frac{4}{3}{\mathrm{\pi r}}^3\times {\mathrm{\rho }}_{\mathrm{air}}\mathrm{g}$

$4{\mathrm{\pi r}}^2{\mathrm{t\rho }}_{\mathrm{s}}=\frac{4}{3}{\mathrm{\pi r}}^3{\mathrm{\rho }}_{\mathrm{He}}\mathrm{g}\left({\mathrm{\rho }}_{\text{air }}-{\mathrm{\rho }}_{\mathrm{He}}\right)$

$\mathrm{t}=\frac{\mathrm{r}}{3{\mathrm{\rho }}_{\mathrm{s}}}\left({\mathrm{\rho }}_{\text{air }}-{\mathrm{\rho }}_{\mathrm{He}}\right)$

$\mathrm{\rho }=\frac{\mathrm{PM}}{\mathrm{RT}}$

$=\frac{\mathrm{r}}{3{\mathrm{\rho }}_{\mathrm{s}}\mathrm{RT}}\left({\mathrm{P}}_{\text{air }}\times {\mathrm{M}}_{\text{air }}-{\mathrm{P}}_{\mathrm{He}}{\mathrm{M}}_{\mathrm{He}}\right)$

$=\frac{{10}^{-2}}{3\times {10}^3\times 300\times \frac{25}{3}}\left(20\times 30\times {10}^{-3}-50\times 4\times {10}^{-3}\right)$

$=\frac{{10}^{-10}}{75}\left(400\right)$

$=\frac{4\times 4\times {10}^{-8}}{75\times 4}=\frac{16}{3}\times {10}^{-10}$

$\mathrm{p}=20+4\times \frac{\frac{4}{40}}{{10}^{-2}}=50$

$\mathrm{mg}+\frac{4}{3}{\mathrm{\pi r}}^3{\mathrm{\rho }}_{\mathrm{He}}\mathrm{g}=\frac{4}{3}{\mathrm{\pi r}}^3\times {\mathrm{\rho }}_{\mathrm{air}}\mathrm{g}$

$4{\mathrm{\pi r}}^2{\mathrm{t\rho }}_{\mathrm{s}}=\frac{4}{3}{\mathrm{\pi r}}^3{\mathrm{\rho }}_{\mathrm{He}}\mathrm{g}\left({\mathrm{\rho }}_{\text{air }}-{\mathrm{\rho }}_{\mathrm{He}}\right)$

$\mathrm{t}=\frac{\mathrm{r}}{3{\mathrm{\rho }}_{\mathrm{s}}}\left({\mathrm{\rho }}_{\text{air }}-{\mathrm{\rho }}_{\mathrm{He}}\right)$

$\mathrm{\rho }=\frac{\mathrm{PM}}{\mathrm{RT}}$

$=\frac{\mathrm{r}}{3{\mathrm{\rho }}_{\mathrm{s}}\mathrm{RT}}\left({\mathrm{P}}_{\text{air }}\times {\mathrm{M}}_{\text{air }}-{\mathrm{P}}_{\mathrm{He}}{\mathrm{M}}_{\mathrm{He}}\right)$

$=\frac{{10}^{-2}}{3\times {10}^3\times 300\times \frac{25}{3}}\left(20\times 30\times {10}^{-3}-50\times 4\times {10}^{-3}\right)$

$=\frac{{10}^{-10}}{75}\left(400\right)$

$=\frac{4\times 4\times {10}^{-8}}{75\times 4}=\frac{16}{3}\times {10}^{-10}$