Twenty-seven solid iron spheres,each of radius $r$ and surface area $S$,are melted to form a single sphere with surface area $S^{\prime}$. Find the radius $r^{\prime}$ of the new sphere. (in $r$)

Find $(i)$ the curved surface area and $(ii)$ the total surface area of a hemisphere of radius $21\, cm$.

What length of tarpaulin $3\, m$ wide will be required to make a conical tent of height $8\, m$ and base radius $6\, m$ (in $, m$)? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately $20\, cm$ (Use $\pi = 3.14$).

The diameter of the moon is approximately one-fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?

$A$ hemispherical bowl has a radius of $3.5\, cm$. What would be the volume of water it would contain (in $, cm^{3}$)?

The students of a Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base,using cardboard. Each penholder was to be of radius $3 \,cm$ and height $10.5 \,cm$. The Vidyalaya was to supply the competitors with cardboard. If there were $35$ competitors,how much cardboard was required to be bought for the competition (in $,cm^2$)? $\left[\text{Assume } \pi = \frac{22}{7}\right]$