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 \\ \\ (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