A cylindrical glass has inner diameter $5\,\mathrm{cm}$ and height $10\,\mathrm{cm}$, but its bottom has a hemispherical raised portion inside. What is the actual capacity of the glass? Use $\pi=3.14$. 

Apparent capacity of the full cylinder is $\pi r^2h=3.14\times2.5^2\times10=196.25\,\mathrm{cm}^3$. The raised hemisphere reduces capacity by $\frac{2}{3}\pi r^3=\frac{2}{3}\times3.14\times2.5^3=32.71\,\mathrm{cm}^3$. So actual capacity $=196.25-32.71=163.54\,\mathrm{cm}^3$.