Answer:
Scale factor = [tex]\frac{4}{9}[/tex]
Perimeter ratio = 4 : 9
Surface area ratio = 16 : 81
Volume ratio = 64 : 729
Step-by-step explanation:
Volume ratio = [tex]\frac{\text{volume of small prism}}{\text{Volume of large prism}}[/tex]
= [tex]\frac{128}{1458}[/tex]
= [tex]\frac{64}{729}[/tex]
= 64 : 729
Scale factor = [tex]\sqrt[3]{\frac{\text{volume of small prism}}{\text{Volume of large prism}}}[/tex]
= [tex]\sqrt[3]{\frac{64}{729}}[/tex]
= [tex]\frac{4}{9}[/tex]
Perimeter ratio = Scale factor
= [tex]\frac{4}{9}[/tex]
= 4 : 9
Surface area ratio = (Scale factor)²
= [tex](\frac{4}{9})^{2}[/tex]
= [tex]\frac{16}{81}[/tex]
= 16 : 81
