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 $r$)

$A$ cubical box has each edge $10\, cm$ and another cuboidal box is $12.5\, cm$ long,$10\, cm$ wide and $8\, cm$ high. Which box has the greater lateral surface area and by how much (in $, cm^2$)?

In a hot water heating system,there is a cylindrical pipe of length $28 \, m$ and diameter $5 \, cm$. Find the total radiating surface in the system. $\left[ \text{Assume } \pi = \frac{22}{7} \right]$ (in $, m^2$)

The diameter of a sphere is decreased by $25\%$. By what per cent does its curved surface area decrease (in $\%$)?

$A$ conical tent is $10 \, m$ high and the radius of its base is $24 \, m$. Find the cost of the canvas required to make the tent,if the cost of $1 \, m^2$ canvas is $Rs. 70$.

$A$ joker's cap is in the form of a right circular cone of base radius $7\, cm$ and height $24\, cm$. Find the area of the sheet required to make $10$ such caps. (in $, cm^2$)