Three cuboids of dimensions `5c m\ xx\ 6c m\ xx\ 7c m ,\ 4c m\ xx\ 7c m\ xx\ 8c m\ a n d\ 2c m\ xx\ 3c m\ xx\ 13 c m` are melted and a cube is made. Find the side of cube.

Explanation

Given:
Three cuboids of dimensions `5c m\ xx\ 6c m\ xx\ 7c m ,\ 4c m\ xx\ 7c m\ xx\ 8c m\ a n d\ 2c m\ xx\ 3c m\ xx\ 13 c m` are melted and a cube is made.
Volume of first cuboid`=5cmtimes6cmtimes7cm=210cm^3`
Volume of second cuboid`=4cmtimes7cmtimes8cm=224cm^3`
Volume of third cuboid`=2cmtimes3cmtimes13cm=78cm^3`
Now,
Volume of new cube formed`=`Volume of first cube`+`Volume of second cube`+`Volume of third cube
Volume of new cube`=210cm^3+224cm^3+78cm^3`
Volume of new cube`=512cm^3`
As we know that the volume of cube is given by:
`V=a^3` (where `a` is the side of the cube)
`512cm^3=a^3`
`(8cm)^3=a^3`
`a=8cm`
Hence, the side of the new cube formed is `8cm`.