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

The volume of a cylinder is given by:

Write 'True' or 'False' and justify your answer:
The volume of the frustum of a cone is $\frac{1}{3} \pi h[r_{1}^{2} + r_{2}^{2}-r_{1} r_{2}],$ where $h$ is the vertical height of the frustum and $r_{1}, r_{2}$ are the radii of the ends.

Find the number of metallic circular discs with $1.5\, cm$ base diameter and height $0.2\, cm$ that must be melted to form a right circular cylinder of height $10\, cm$ and diameter $4.5\, cm$.

How many balls with diameter $1 \, cm$ can be produced by melting a metallic cylinder with radius $6 \, cm$ and height $4 \, cm$?

Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter $2 \, cm$ and height $16 \, cm$. The diameter of each sphere is (in $cm$):