Find the surface area using volume

Question

A water tank has a surface area of $8000$ cm² and a capacity of $51.2$ liters. Find the surface area of a similar water tank which has a capacity of $21.6$ liters.

Answer 1

Hint:

If both tanks are similar, it means their aspect ratio $^1$ is the same. That means that $V/A$ remains constant for each tank, where $V$ is volume and $A$ is the surface area.

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$^1$, I thinks there's another name for this. Maybe, characteristic length.

Answer 2

HINT:

Surface area $\propto$ side$^2$ and capacity $\propto$ volume $\propto$ side $^3$

$\implies$ Surface area $^3\propto$ capacity $^2$

Answer 3

The volume is scaled by the factor $\frac{1}{2}$. So the linear dimensions are scaled by the factor $\left(\frac{1}{2}\right)^{1/3}$. So surface area is scaled by the factor $\left(\frac{1}{2}\right)^{2/3}$.