A cubical block of side $7 \mathrm{cm}$ is surmounted by a hemisphere. What is the greatest diameter that the hemisphere can have? Also find the surface area of the solid.

A hemispherical and conical hole are scooped out of a solid wooden cylinder. Find the volume of the remaining solid where measurements are as follows:

The height of the cylinder is $7 \mathrm{cm}$, radius of each 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 $\pi =\frac{22}{7}$.

The adjoining figure shows a hemisphere of radius $5 \mathrm{cm}$ surmounted by a right circular cone of base radius $5 \mathrm{cm}$. Find the volume of the solid if the height of the cone is $7 \mathrm{cm}$. Give your answer correct to two places of decimal.