Two solid spheres made of the same metal have weights $5920 \, g$ and $740 \, g$ respectively. Determine the radius of the larger sphere,if the diameter of the smaller one is $5 \, cm$. (in $cm$)

The water for a factory is stored in a hemispherical tank whose internal diameter is $14\, m$. The tank contains $50\, kilolitres$ of water. Water is pumped into the tank to fill it to its capacity. Calculate the volume of water pumped into the tank (in $m^3$).

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

The radius and height of a cylindrical coin are $1.4 \, cm$ and $0.1 \, cm$ respectively. $60$ such coins are stacked up to make a larger cylindrical pillar. Find the volume of this larger cylinder (in $cm^3$).

$A$ small village, having a population of $5000$, requires $130\, \text{litres}$ of water per head per day. The village has an overhead cuboidal tank measuring $20\, \text{m} \times 13\, \text{m} \times 10\, \text{m}$. For how many days will the water of this tank last?

The surface area and volume of a cube with an edge length of $x \ cm$ are numerically equal. Find the value of $x$.