The volume of the box with base area [tex] A [/tex] and height [tex] h [/tex] is
[tex] V=Ah [/tex].
The volumes of the box with base area [tex] 2*2 [/tex] and with base area [tex] 4*4 [/tex] are the same. Let [tex] h_1,h_2 [/tex] be the heights of the box with smaller base area and larger base area respectively. Then,
[tex] V=2*2h_1=4*4h_2\\
\frac{h_1}{h_2}=\frac{16}{4}\\
\frac{h_1}{h_2}=4
[/tex].
Thus the height of the box with smaller base area is [tex] 4 [/tex] times that of the box with larger base area.
