A shed is shaped like a cuboid surmounted by a half cylinder, as shown in the figure. The base of the cuboid is $7\,\mathrm{m}\times 15\,\mathrm{m}$ and its height is $8\,\mathrm{m}$. What is the volume of air the empty shed can hold? Take $\pi=\frac{22}{7}$. 

The shed's volume is the sum of the cuboid and the half-cylinder. Cuboid volume $=15\times7\times8=840\,\mathrm{m}^3$. The half-cylinder has radius $3.5\,\mathrm{m}$ and length $15\,\mathrm{m}$, so its volume is $\frac12\pi r^2h=\frac12\times\frac{22}{7}\times3.5^2\times15=288.75\,\mathrm{m}^3$. Total volume $=840+288.75=1128.75\,\mathrm{m}^3$.