Answer:
The ratio of the volumes is 8/125
Explanation:
Given:
The ratio of the sides of two similar triangles = 2/5
To find:
the ratio of the volumes
The ratio of the sides (length) of similar shapes is known as the scale factor
[tex]\begin{gathered} Scale\text{ factor = }\frac{length\text{ of one side}}{length\text{ of its corresponding sides}} \\ \\ scale\text{ factor = }\frac{2}{5} \end{gathered}[/tex]
The volume of the ratio is the cube of the scale factors
To get the ratio of the volumes, we will cube the ratio given:
[tex]\begin{gathered} Ratio\text{ of the volumes = \lparen scale factor\rparen}^3 \\ \\ Ratio\text{ of the volumes = \lparen}\frac{2}{5})^3 \end{gathered}[/tex][tex]\begin{gathered} Ratio\text{ of the volumes = }\frac{2^3}{5^3} \\ \\ Ratio\text{ of the volumes = }\frac{8}{125} \end{gathered}[/tex]
