I have following problem
How many cubes, each with surface area of 36 square centi. are needed to form 2 cubes , each with surface area of 144 square centimeter
To me, i would just divide 144*2 / 36 to get 8 cubes, however the result has 16 as correct answer. What is the logic i am missing?
On
The cube with surface area $36$ square cm has side length $\sqrt {6}$ cm, while the cube with surface area $144$ square cm has side length $\sqrt {24}=2\sqrt {6}$ cm.
On
If you scale an object by a factor of $s$, then the surface changes by $s^2$, but the volume by $s^3$ (square-cube law).
Thus, if we increase the surface from $36$ to $144$, the corresponding scaling factor is:
$$s^2 = \frac{144}{36} = 4 \ \ \Rightarrow \ \ s = \sqrt{4} = 2$$
The volume changes by $s^3 = 2^3 = 8$.
Therefore, we can fit 8 small cubes into the large cube and $16$ into two of them.
You can't directly divide the areas because when you combine the cubes together, some faces go inside and only the ones left on the outside count. So, first you find the side lengths of the cubes, which are $\sqrt6$ and $2\sqrt6$ respectively.
With some imagination you can see that 8 smaller cubes together will form one bigger cube of side length twice the smaller ones. So for two of them you need total 16 cubes.