A cube with edges of length b is divided into 8 equal smaller cubes. What is the difference between the combined surface area of the 8 smaller cubes and the surface area of the original cube ?

Options

A. `(3)/(2)b^(2)`
B. `(3)/(4)b^(2)`
C. `(9)/(2)b^(2)`
D. `6b^(2)`

Answer

D

Explanation

When a cube of edge length b is divided into 8 identical smaller cubes, the edge of each of the smaller cubes is `(b)/(2)`.
The surface area of the original cube is `6xxb xxb=6b^(2)`.
The surface area of one of the smaller cubes is `6xx(b)/(2)xx(b)/(2)=(6b^(2))/(4)` or `(3b^(2))/(2)`. There are eight small cubes, so their combined surface area is `8((3b^(2))/(2))=12b^(2)`. The difference is `12b^(2)-6b^(2)=6b^(2)`.