Find the lateral surface area of the cuboid which measures $50 \, cm \times 40 \, cm \times 30 \, cm$. (in $cm^2$)

The edges of three of the four cubes are $1\, cm, 9\, cm$ and $10\, cm$ respectively. If the total volume of two cubes with $9\, cm$ edge and $10\, cm$ edge is equal to the volume of the remaining two cubes,find the edge of the fourth cube in $cm$.

$1\, m^{3} = \dots \, cm^{3}$

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

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

State whether the following statement is true or false:
The ratio of the surface areas of two spheres is $81: 49$. Then,the ratio of their volumes is $729: 343$.