Question

Consider a cube of edge length 1 cm. The total surface area of the same material if it were subdivided into colloidal size cubes each having an edge length of ${10}^{-7}$ cm is $y\times {10}^7$ sq cm. What is $y$?

Answer 1

Surface area of cube of edge length $1cm$ $=(6\times 1)c{m}^2$.

Surface area of cube of edge length ($1\times {10}^{-7})cm=(6\times {10}^{-14})c{m}^2$.

Let $n$ cubes of $6\times {10}^{-14}c{m}^2$ are present on breaking the cube of $6c{m}^2$.

$\therefore n\times$ volume of cube of edge length ${10}^{-7}cm=$ Volume of cube of edge length $1cm$.

$n\times [{10}^{-7}{]}^3=(1{)}^3$

$\therefore n={10}^{21}$

$\therefore$ New total surface area $={10}^{21}\times 6\times {10}^{-14}=6\times {10}^7$.

So, the value of $y$ is $6$.