The base of a cone is hemispherical. The radius of the cone is $15 \, cm$ and the total height of the solid is $55 \, cm$. Find the volume of this solid (in $cm^3$).

$A$ solid metallic hemisphere of radius $8 \, cm$ is melted and recast into a right circular cone of base radius $6 \, cm$. Determine the height of the cone (in $cm$).

$A$ pen stand made of wood is in the shape of a cuboid with four conical depressions and a cubical depression to hold the pens and pins,respectively. The dimensions of the cuboid are $10 \, cm$,$5 \, cm$,and $4 \, cm$. The radius of each of the conical depressions is $0.5 \, cm$ and the depth is $2.1 \, cm$. The edge of the cubical depression is $3 \, cm$. Find the volume of the wood in the entire stand. (in $, cm^3$)

$A$ toy is in the form of a cone surmounted on a hemisphere. The radius of the cone as well as the hemisphere is $3.5\, cm$ and the total height of the toy is $15.5\, cm$. Find its total surface area (in $cm^2$).

For a cone,$l = \ldots \ldots \ldots \ldots$

$A$ cylindrical pencil sharpened at one edge is the combination of