If a marble of radius $2.1 \, cm$ is put into a cylindrical cup full of water of radius $5 \, cm$ and height $6 \, cm$,then how much water flows out of the cylindrical cup? (in $cm^3$)

$A$ cylinder is closed at both ends by hemispheres. The radius of the cylinder is $21 \, cm$ and the total height of the article is $92 \, cm$. Find the total surface area of the article (in $cm^2$).

$A$ metallic cylinder with radius $15\, cm$ and height $20\, cm$ is melted and recast to produce identical balls with radius $3\, cm$. Find the number of balls produced.

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

The ratio of the diameters of two cylinders is $3:4$ and the ratio of their heights is $4:5$. Then,the ratio of their volumes is ..... .

$A$ cylinder is closed at both ends by $12 \, cm$ high cones. The radius of the cylinder is $5 \, cm$ and the total height of the article is $41 \, cm$. Find the total surface area of the article. $(\pi = 3.14)$ (in $cm^2$)