A hemispherical and a conical hole is scooped out of a solid wooden cylinder. Find the volume of the remaining solid where the measurements are as follows:
The height of the solid cylinder is $7\mathrm{cm}$, radius of each of hemisphere, cone and cylinder is $3\mathrm{cm}$. Height of cone is $3\mathrm{cm}$.
Give your answer correct to the nearest whole number. Take $\mathit{\pi }=\frac{22}{7}$.