PX275 - B4e - pappus's first theorem

d V = 2 π y d A

\bar{y} = \frac{1}{A} \iint y d A

V = 2 π A \bar{y}

\bar{y} = \frac{V_{s p h e r e}}{2 π A_{s e m i c i r c l e}} = \frac{\frac{4}{3} π a^{3}}{2 π \frac{π a^{2}}{2}}

∴ \bar{y} = \frac{4 a}{3 π}