What is the surface area of a cube having an edge length of 1 cm? What would be 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 ?

Explanation

Surface area of a cube `=6l ^(2)=6xx(1cm)^(2)=6cm^(2)`
Volume of cube of edge length `1 cm =l^(3)=1 cm^(3)`
Volume of cube of edge length `10^(-7)cm =(10^(-7))^(3)=10^(-21)cm^(3)`
`therefore` No. of smaller cubes in big cube `=(1)/(10^(-21))=10^(21)`
Surface area of each smaller cube `=6l^(2)=6(10^(21))^(2)=6xx10^(-14)cm^(2)`
`therefore` Total surface area of all the smaller cuber `=(10^(21))xx(6xx10^(-14))cm^(2)=6xx10^(7)cm^(2)`