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

The areas of the three adjacent faces meeting at one vertex of a cuboid are $4000 \, cm^2$,$2000 \, cm^2$,and $3200 \, cm^2$ respectively. Find the dimensions and the volume of the cuboid.

$A$ storage tank is in the form of a cube. When it is full of water, the volume of water is $15.625 \, m^3$. If the present depth of water is $1.3 \, m$, find the volume of water already used from the tank (in $m^3$).

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

Find the volume of a sphere of radius $2.1 \, cm$. (in $cm^3$)

Metal spheres,each of radius $2 \, cm$,are packed into a rectangular box of internal dimensions $16 \, cm \times 8 \, cm \times 8 \, cm$. When $16$ spheres are packed,the box is filled with preservative liquid. Find the volume of this liquid. Give your answer to the nearest integer. [Use $\pi = 3.14$] (in $cm^3$)