Eight identical cuboidal wooden blocks are stacked one on top of the other. The total volume of the solid so formed is `128\ c m^3dot` If the height of each block is 1cm and the base is a square, find the dimensions of each block.

Explanation

Given:
The total volume of the solid so formed is `128\ c m^3`.
The height of each block is `1 cm` and the base is a square.
Let `l` and `b` of square base be `x cm` each.
Height of `1` box is `1 cm`.
`therefore` Height of `8` box will be `8times1 cm=8 cm`.
Now,
Volume of block`=xtimesxtimes8`
`128=8x^2`
`x^2=128/8`
`x^2=16`
`x=sqrt(16)`
`x=4cm`
`therefore`Dimensions are:
Length`=x=4 cm`
Breadth`=x=4 cm`
Height`=1 cm`
Hence, the dimensions of the cuboidal block is `4 cmtimes4 cmtimes1 cm`.