Respuesta :
Answer:
Scale factor of cube to the smaller cube is 5 : 3.
Step-by-step explanation:
Ratio of the volumes of two cubes = [tex]\frac{\text{volume of large prism}}{\text{Volume of small prism}}[/tex]
= [tex]\frac{1000}{216}[/tex]
= [tex]\frac{125}{27}[/tex]
Scale factor of these cubes = [tex]\sqrt[3]{\text{ratio of the volumes of the cubes}}[/tex]
= [tex]\sqrt[3]{\frac{\text{volume of large prism}}{\text{Volume of small prism}}}[/tex]
= [tex]\sqrt[3]{\frac{125}{27} }[/tex]
= [tex]\frac{5}{3}[/tex]
= 5 : 3
Therefore, scale factor of cube to the smaller cube is 5 : 3.
