The radii of three metallic spheres are $3 \, cm$,$4 \, cm$,and $5 \, cm$. These spheres are melted and recast into a single new sphere. Find the radius of the new sphere (in $cm$).

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

$500$ persons are taking a dip into a cuboidal pond which is $80 \, m$ long and $50 \, m$ broad. What is the rise of water level in the pond,if the average displacement of the water by a person is $0.04 \, m^3$? (in $cm$)

The $CSA$ and the volume of a cylinder are numerically equal. Then,its radius is $\ldots \ldots \ldots \ldots$ units.

$A$ metallic sphere with radius $18 \,cm$ is melted and recast to produce cylinders with radius $3 \,cm$ and height $12 \,cm$. Find the number of cylinders produced.

$A$ cylindrical tank is closed at both the ends by cones of height $12 \, cm$. The diameter of the cylindrical part is $14 \, cm$ and its height is $20 \, cm$. Find the volume of this tank (in $cm^3$).