A factory manufactures cube-shaped containers, with each side measuring $7 \mathrm{cm}$. If the product filled in the container occupies $\frac{3}{4}\mathrm{th}$ of the container, what is the volume of air left in it? If $150.5$ $\mathrm{cu}. \mathrm{cm}.$ of air is required to keep the product fresh for a week, will the food inside the container be edible after a week?

The volume of a cube is $1000 {\mathrm{cm}}^3$. Find its side.

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

A hall is $15 \mathrm{m}$ long and $12 \mathrm{m}$ broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of the four walls, the volume of the hall in $\mathrm{cu} \mathrm{m}$ is

A metal cube is completely submerged in a cylindrical vessel containing water. The diameter of the vessel is $30cm,$ the level of water is raised by $1\frac{41}{99} cm$ . The length of the edge of the cube is: