$A$ solid cylinder has a total surface area of $231 \, cm^2$. Its curved surface area is $(2/3)$ of the total surface area. Find the volume of the cylinder (in $cm^3$).

The length of the diagonal of a cube is $6 \text{ cm}$. The volume of the cube (in $\text{cm}^3$) is (in $\sqrt{3}$)

Consider the volumes of the following:
$1.$ $A$ parallelepiped of length $5\,cm$,breadth $3\,cm$ and height $4\,cm$.
$2.$ $A$ cube of each side $4\,cm$.
$3.$ $A$ cylinder of radius $3\,cm$ and length $3\,cm$.
$4.$ $A$ sphere of radius $3\,cm$.
The volumes of these in decreasing order are:

$A$ solid sphere and a solid hemisphere have the same total surface area. The ratio of their volumes is

The volumes of two cubes are in the ratio of $8: 125$. Find the ratio of their edges and surface areas.

$A$ cylindrical vessel of radius $4 \, cm$ contains water. $A$ solid sphere of radius $3 \, cm$ is lowered into the water until it is completely immersed. The water level in the vessel will rise by (in $cm$)