Let's say the length of the small box is x. We assume it's a cube, so all the dimensions are equal.
Now, the volume of the cube equals the product of its dimensions:
V = length . length . length = length³
So, the volume of the large box is:

As we know this volume is 243, we have:
![\begin{gathered} 243=(3x)^3 \\ \sqrt[3]{243}=3x \\ x\text{ = }\frac{\sqrt[3]{243}}{3} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/t4h8ozmgguqs7ibqyp1fzoazj1fnelq74f.png)
Now you use the value of x to find the volume of the smaller box:
![V_s=x^3=\frac{\sqrt[3]{243}^3}{3^3}=\frac{243}{3^3^{}}=(243)/(27)=9](https://img.qammunity.org/2023/formulas/mathematics/college/ywg02pnkrtwszu1ys6unppfcdktdxca8za.png)