If two solid hemispheres of same base radius $r$ are joined together along their bases, then the curved surface area of this new solid is (in $\pi r^{2}$)

$A$ cone of maximum size is carved out from a cube of edge $14 \, cm$. Find the surface area of the cone and the surface area of the remaining solid left after the cone is carved out.

$A$ top is made by joining a hemisphere to the base of a cone. The radius and the height of the conical part are $2.8 \, cm$ and $6.4 \, cm$ respectively. Find the volume of the top in $cm^3$.

Two cones with the same base radius $8\, cm$ and height $15\, cm$ are joined together along their bases. Find the surface area of the shape so formed. (in $cm^2$)

$A$ 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 $, cm^3$)

$A$ metallic cylinder with diameter $1 \, cm$ and height $4 \, cm$ is melted and recast to produce balls of radius $\frac{1}{8} \, cm$. Find the number of balls produced.