The volume of a sphere is $4500 \pi \text{ cm}^3$,then its diameter is $\dots \text{ cm}$.

State whether the following statement is True or False and justify your answer: If the radius of a cylinder is doubled and its height is halved,the volume will be doubled.

The surface area of a sphere and the curved surface area of a hemisphere are equal. Find the ratio of their radii.

The total surface area of a cube is $864 \, cm^2$. Then its edge is $\ldots \ldots \ldots \, cm$.

The total surface area of a closed cylinder is $748\, cm^2$. If its radius is $7\, cm$,find its height (in $cm$).

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 $cm^{2}.$