Question

Suppose you have two similar rectangular prisms. The volume of the smaller rectangular prism is 125 in^3 and the volume of the larger rectangular prism is 729 in^3. What is the scale factor of the smaller figure to the larger figure. PLZZZ ANSWER ASAP!!!

Answer 1

Answer:

$\boxed{ \frac{ 5}{ 9}}$

Step-by-step explanation:

Data:

V₁ = 125 in³

V₂ = 729 in³

Calculations:

A scale factor (C) is the ratio of corresponding side lengths (l) of the two prisms.

$C=\frac{ l_{1}}{ l_{2}}$

The volume ratio is the cube of the scale factor.

$\frac{V_{1}}{ V_{2}} = C^{3}$

$\frac{125}{ 729} = C^{3}$

$C = \sqrt [3]{\frac{ 125}{729 }} = \frac{5 }{9 }$

$\boxed{ \textbf{The scale factor is } \frac{ 5}{ 9}.}$