A solid metallic block of volume $2$ cubic metres is melted and recast into a rectangular bar of length $32 \mathrm{m}$ having a square base. If the weight of the block is $160 \mathrm{kg}$ and the biggest cube is cut off from the bar then what is the weight of the cube is?

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 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:

If side of each cube is $3 \text{cm}$. Then Volume of given figure is 

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

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