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Alexxandr [17]2 years ago

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Answer:

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Scale factor of cube to the smaller cube is 5 : 3.

Step-by-step explanation:

Ratio of the volumes of two cubes = $\frac{\text{volume of large prism}}{\text{Volume of small prism}}$

= $\frac{1000}{216}$

= $\frac{125}{27}$

Scale factor of these cubes = $\sqrt[3]{\text{ratio of the volumes of the cubes}}$

= $\sqrt[3]{\frac{\text{volume of large prism}}{\text{Volume of small prism}}}$

= $\sqrt[3]{\frac{125}{27} }$

= $\frac{5}{3}$

= 5 : 3

Therefore, scale factor of cube to the smaller cube is 5 : 3.

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