The dome of a building is in the form of a hemisphere. Its radius is $4.2 \, m$. Find the cost of painting it at the rate of ₹ $18$ per $m^2$. (in ₹)

If $V$ is the volume of a cuboid of dimensions $a, b, c$ and $S$ is its total surface area,then prove that $\frac{1}{V} = \frac{2}{S} \left( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \right)$.

Find the total surface area of a hemisphere of radius $42 \, cm$. (in $cm^2$)

The length and breadth of a cuboid are $30\, cm$ and $25\, cm$. If the total surface area of the cuboid is double the lateral surface area of the cuboid,find its height and volume.

$A$ cylindrical container of radius $14\, cm$ is partially filled with water. $A$ solid cuboid of iron with dimensions $22\, cm \times 16\, cm \times 7\, cm$ is submerged in it. Find the rise in the level of the water when the solid is completely submerged. (in $cm$)

The volume of a cube is $3375\, cm^{3}$. Find its edge and total surface area.