The diameter of a solid hemisphere is $21 \, cm$,then its volume is $\ldots \ldots \ldots \, cm^3$.

Rain water which falls on a flat rectangular surface of length $6\, m$ and breadth $4\, m$ is transferred into a cylindrical vessel of internal radius $20\, cm$. What will be the height of water in the cylindrical vessel if the rainfall is $1\, cm$? Give your answer to the nearest integer. (Take $\pi = 3.14$) (in $cm$)

In $\Delta ABC$,$\angle B = 90^{\circ}$,$AB = 6.3 \, cm$,and $BC = 8.4 \, cm$. If the triangle is revolved about the side $AB$,find the volume of the cone so obtained. Similarly,if the triangle $ABC$ is revolved about the side $BC$,find the volume of the cone so obtained.

The front compound wall of a house is decorated by wooden spheres of diameter $21\, cm,$ placed on small supports as shown in the figure. Eight such spheres are used for this purpose,and are to be painted silver. Each support is a cylinder of radius $1.5\, cm$ and height $7\, cm$ and is to be painted black. Find the cost of paint required if silver paint costs $25$ paise per $cm^{2}$ and black paint costs $5$ paise per $cm^{2}.$

Two solid spheres made of the same metal have weights $5920\, g$ and $740\, g$ respectively. Determine the radius of the larger sphere,if the diameter of the smaller one is $5\, cm$. (in $cm$)

$1 \, m^{2} = \ldots \ldots \, cm^{2}$