Question

How many times as tall is the box with the smaller base

Answer 1

We have the following boxes:

We know that the volume of both boxes is the same, then we have the following expression:

`V_h=V_H`

then, in this case we have the following:

`\begin{gathered} V_h=(5)^2\cdot h \\ V_H=(10)^2\cdot H \\ V_h=V_H \\ \Rightarrow(5)^2\cdot h=(10)^2\cdot H \\ \Rightarrow h=(100H)/(25)=4H \\ h=4H \end{gathered}`

therefore, the box with the smaller base is 4 times taller than the box with the bigger base