The capacity of a cuboidal water tank is $60,000$ litres. If its length is $5$ m and breadth is $4$ m, find its height in meters.

The edge of a cube is $6 \, cm$. Find the total surface area of the cube and the volume of the cube.

The volume of a cuboid with length $25\, cm$ and breadth $15\, cm$ is equal to the volume of a cube with edge $15\, cm$. Find the height of the cuboid (in $cm$).

$A$ wooden bookshelf has external dimensions as follows: Height $= 110\, cm$,Depth $= 25\, cm$,Breadth $= 85\, cm$ (see Fig.). The thickness of the plank is $5\, cm$ everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is $20$ paise per $cm^2$ and the rate of painting is $10$ paise per $cm^2$,find the total expenses required for polishing and painting the surface of the bookshelf.

The curved surface area of a cylinder is $550 \, cm^2$. If its height is $50 \, cm$,find its diameter in $cm$.

$1\, m^{3} = \dots \, cm^{3}$