Respuesta :
ANSWER :
The answers are :
A. k = 8
B. k = 1/4
C. k = 1
EXPLANATION :
Note that dilation of surface areas :
[tex]\begin{gathered} \sqrt{S_n}=k\sqrt{S_o} \\ k=\sqrt{\frac{S_n}{S_o}} \end{gathered}[/tex]in which Sn is the new image
So is the original image
and k is the scale factor.
From the problem, we have So = 8 square units
A. Sn = 512 square units :
[tex]\begin{gathered} k=\sqrt{\frac{S_n}{S_o}} \\ k=\sqrt{\frac{512}{8}} \\ k=8 \end{gathered}[/tex]B. Sn = 1/2 square unit
[tex]\begin{gathered} k=\sqrt{\frac{\frac{1}{2}}{8}} \\ k=\frac{1}{4} \end{gathered}[/tex]C. Sn = 8 square units :
[tex]\begin{gathered} k=\sqrt{\frac{8}{8}} \\ k=1 \end{gathered}[/tex]