How many balls with diameter $0.5\, cm$ can be produced by melting a metallic cylinder with radius $2\, cm$ and height $8\, cm$?

$A$ pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are $15 \, cm$ by $10 \, cm$ by $3.5 \, cm$. The radius of each of the depressions is $0.5 \, cm$ and the depth is $1.4 \, cm$. Find the volume of wood in the entire stand (in $cm^3$). [Take $\pi = \frac{22}{7}$]

$A$ metallic sphere of radius $4.2 \, cm$ is melted and recast into the shape of a cylinder of radius $6 \, cm$. Find the height of the cylinder. (in $cm$) [Take $\pi = \frac{22}{7}$]

$A$ cylinder is closed at both the ends by hemispheres. The radius of the cylinder is $4.2 \, cm$ and the total height of the solid is $15 \, cm$. Find the volume of this solid (in $cm^3$).

The shape of a lump of jaggery is that of a frustum of a cone. Its radii are $14 \, cm$ and $7 \, cm$ and height is $12 \, cm$. Find the volume of the lump of jaggery (in $cm^3$).

The diameter of a cylinder is $14\, cm$ and its height is $10\, cm$. Then,the volume of the cylinder is $\ldots \ldots \ldots \ldots cm^3$.