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

$A$ cylinder with radius $14 \, cm$ is closed at one end by a $48 \, cm$ high cone and at the other end by a hemisphere. If the height of the cylinder is $22 \, cm$,find the total surface area of the article (in $cm^2$).

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.

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

Write 'True' or 'False' and justify your answer:
$A$ spherical steel ball is melted to make eight new identical balls. Then,the radius of each new ball is $\frac{1}{8}$th the radius of the original ball.

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 $cm$).