A solid cylinder of radius $r$ and height $h$ is placed over the cylinder of same height and radius. The total surface area of the shape so formed is $4\mathrm{\pi }rh+4\mathrm{\pi }{r}^2.$

The capacity of a cylindrical vessel with a hemispherical portion raised upward at the bottom as shown in the figure is $\frac{\pi r^2}{3}\left[3h-2r\right].$

The curved surface area of a cone is $\pi l\left(r_1+r_2\right)$, where $l=\sqrt{h^2+{\left(r_1+r_2\right)}^2 }$, $r_1$ and $r_2$ are the radius of the two ends of the frustum and $h$ is the vertical height.

Three metallic solid cubes whose edges are $3 \mathrm{cm}, 4 \mathrm{cm}$ and $5 \mathrm{cm}$ are melted and formed into a single cube. Find the edge of the cube so formed.

How many shots having diameter $3 \mathrm{cm}$ can be made from a cuboidal lead solid of dimensions $9 \mathrm{cm}\times 11 \mathrm{cm}\times 12 \mathrm{cm}$?