Nathan, an engineering student was asked to make a model shaped like a cylinder with two cones attached at its two ends. The diameter of the model is $3 \mathrm{cm}$ and its length is $12 \mathrm{cm}$. If each cone has a height of $2 \mathrm{cm},$ find the volume of the model that Nathan made.

A solid consisting of a right circular cone of height $12 \mathrm{cm}$ and radius $6 \mathrm{cm}$ standing on a hemisphere of radius $6 \mathrm{cm}$ is placed upright in a right circular cylinder full of water such that it touches the bottom. The volume of the water displaced out of the cylinder, if the radius of the cylinder is $6 \mathrm{cm}$ and height is $18 \mathrm{cm}$ is $k {\mathrm{cm}}^3$. Find the value of $k$.

As shown in figure a cubical block of side $7 \mathrm{cm}$ is surmounted by a hemisphere. If the surface area of the solid is $A {\mathrm{cm}}^2$, then find the value of $A$.