Question

how many times greater is the volume of the new crate?

Answer 1

$8$

1) We need to get some measures to this crate so that we can get to know the answer.

2) Consider a crate like a rectangular prism, with the following measures:

$\begin{gathered} width=4 \\ height=6 \\ length=8 \end{gathered}$

So now, let's apply to these measurements the proposed transformations:

This would yield the following:

$\begin{gathered} w_2=8 \\ h_2=12 \\ l_2=16 \end{gathered}$

3) Finally, the volume of a rectangular prism is given by the product of their dimensions, so let's compare both:

$\begin{gathered} V_1=4\cdot6\cdot8,\:V_1=192u³ \\ V_2=8\cdot12\cdot16,V_2=1536u³ \\ \\ \frac{1536}{192}=8 \end{gathered}$

Therefore by dividing the augmented volume by the original one we can tell the answer is:

$8$

Because 2³=8