$A$ metallic sphere with radius $42\, cm$ is melted to cast $8000$ identical balls. Find the radius of these balls (in $cm$).

Which of the following correctly matches the information given in Part $I$ and Part $II$?

Part $I$	Part $II$
$1.$ $CSA$ of a cylinder	$a.$ $3\pi r^2$
$2.$ $CSA$ of a sphere	$b.$ $2\pi rh$
$3.$ $CSA$ of a cone	$c.$ $4\pi r^2$
$4.$ $TSA$ of a hemisphere	$d.$ $\pi rl$

$A$ 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 $, cm^3$)

The volume of the largest right circular cone that can be cut out from a cube of edge $4.2 \,cm$ is (in $cm^3$)

$A$ cylindrical bucket of height $32 \,cm$ and base radius $18 \,cm$ is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is $24 \,cm$,find the radius and slant height of the heap.

The volume of a cone with radius $5 \, cm$ and height $12 \, cm$ is ........ $\pi \, cm^{3}$.