The curved surface area of a cone is $550 \, cm^2$. If the radius of the cone is $7 \, cm$,find its volume in $cm^3$.

$30$ circular plates,each of radius $14\,cm$ and thickness $3\,cm$,are placed one above the other to form a cylindrical solid. Find:
$(i)$ the total surface area
$(ii)$ the volume of the cylinder so formed.

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.

$A$ sphere and a cylinder of the same radius have equal volumes. By what percentage does the diameter of the cylinder exceed its height?

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

Find the curved surface area and the total surface area of a hemisphere with a diameter of $14 \, cm$.