Question

5. Raul has two boxes. The large box has dimensions that are 3 times the length of the small box. Thelarger box has a volume of 243 in? What is the volume of the smaller box?

Answer 1

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:

`V_L=(3x)^3`

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}`

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`