Answer:
The surface area of box 1 is 16 times greater than the surface area of box 2
Step-by-step explanation:
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor
Let
z ---> the scale factor
In this problem th[tex]z=4[/tex]e scale factor is equal to 4
so
[tex]z=4[/tex]
step 2
How many times greater is the surface area of box 1 than the surface area of box 2?
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
so
Let
z ----> the scale factor
x ----> surface area of box 1
y ---> surface area of box 2
so
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]z=4[/tex]
substitute
[tex]4^{2}=\frac{x}{y}[/tex]
[tex]16=\frac{x}{y}[/tex]
[tex]x=16y[/tex]
therefore
The surface area of box 1 is 16 times greater than the surface area of box 2
