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 …

Question

asked Feb 20, 2020 166k views

1 Answer

Xiaoyu Yu · Answer 1 · 2020-02-26T06:22:12+0000

Answer:

$\boxed{ ( 5)/( 9)}\\$

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.

$C=( l_(1))/( l_(2))\\$

The volume ratio is the cube of the scale factor.

$(V_(1))/( V_(2)) = C^(3)\\$

$(125)/( 729) = C^(3)\\$

$C = \sqrt [3]{( 125)/(729 )} = (5 )/(9 )\\$

$\boxed{ \textbf{The scale factor is } ( 5)/( 9).}\\$