The radii of two cylinders are in the ratio of $2:3$ and their heights are in the ratio of $5:3$. The ratio of their volumes is

The length of a metal hollow cylinder is $70\, cm$. If the radius of the hollow inside it is $10\, cm$ and the metal thickness is $1\, cm$,find the difference between the areas of the outer and inner curved surfaces.

$A$ metal sphere of radius $20\, cm$ is melted and then cast into small hemispheres each of radius $5\, cm$. Find the number of hemispheres thus obtained (in balls).

The radius and the slant height of a cone are in the ratio $4: 7$. The ratio of its total surface area to its curved surface area is $\ldots \ldots \ldots$

The dimensions of each iron hollow box are $30 \, cm \times 15 \, cm \times 10 \, cm$. What is the volume of a carton containing $60$ such boxes? (in $m^3$)

If $V$ is the volume of a cuboid of dimensions $a, b, c$ and $S$ is its total surface area,then prove that $\frac{1}{V} = \frac{2}{S} \left( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \right)$.