$3$ solid cubes whose edges are $6, 8$ and $10 \, cm$ respectively,are melted and formed into a single cube. If there is no loss of metal in the process,find the edge of the new cube (in $cm$).

The total surface area of a hemisphere is $41.58 \text{ cm}^2$. Find its curved surface area (in $\text{cm}^2$).

Consider the volumes of the following:
$1.$ $A$ parallelepiped of length $5\,cm$,breadth $3\,cm$ and height $4\,cm$.
$2.$ $A$ cube of each side $4\,cm$.
$3.$ $A$ cylinder of radius $3\,cm$ and length $3\,cm$.
$4.$ $A$ sphere of radius $3\,cm$.
The volumes of these in decreasing order are:

$A$ roller is $120 \, cm$ long and has a diameter of $84 \, cm$. If it takes $500$ complete revolutions to level a playground,determine the cost of levelling at the rate of $30 \, \text{paise}$ per $m^2$ (in $Rs.$). (Use $\pi = \frac{22}{7}$)

$A$ tent is in the shape of a right circular cylinder up to a height of $3\, m$ and then becomes a right circular cone with a maximum height of $13.5\, m$ above the ground. If the radius of the base is $14\, m$,find the cost of painting the inner side of the tent at the rate of ₹ $2$ per $m^2$ (in ₹).

$A$ right circular cylindrical tunnel of diameter $5\, m$ and length $10\, m$ is to be constructed from a sheet of iron. The area of iron sheet required will be..........$\pi\, m^2$.