$A$ solid cube of side $12 \, cm$ is cut into eight cubes of equal volume. What will be the side of the new cube? Also,find the ratio between their surface areas.

Find the surface area of a sphere of diameter $21 \, cm$. Assume $\pi = \frac{22}{7}$. (in $, cm^{2}$)

Find the surface area of a sphere of radius $14 \, cm$.
Assume $\pi = \frac{22}{7}$. (in $, cm^2$)

$A$ child is playing with building blocks, which are in the shape of cubes, and has built a structure as shown in the figure. If the edge of each cube is $3 \, cm$, find the volume of the structure built by the child. (in $cm^3$)

$A$ cuboidal vessel is $10 \, m$ long and $8 \, m$ wide. How high must it be made to hold $380$ cubic metres of a liquid (in $, m$)?

$A$ 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.