Respuesta :

[tex]\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\\\ \begin{array}{ccccllll} &\stackrel{\stackrel{ratio}{of~the}}{Sides}&\stackrel{\stackrel{ratio}{of~the}}{Areas}&\stackrel{\stackrel{ratio}{of~the}}{Volumes}\\ \cline{2-4}&\\ \cfrac{\stackrel{similar}{shape}}{\stackrel{similar}{shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}~\hspace{6em} \cfrac{s}{s}=\cfrac{\sqrt{Area}}{\sqrt{Area}}=\cfrac{\sqrt[3]{Volume}}{\sqrt[3]{Volume}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \cfrac{s}{s}=\cfrac{\sqrt[3]{8}}{\sqrt[3]{125}}\implies \cfrac{s}{s}=\cfrac{2}{5}\qquad \leftarrow \textit{ratio of the sides or scale factor}[/tex]

The required scale factor for the two similar cylinders with the volume of one is 8cm^3, and the volume of the other is 125cm^3 is 2 / 5.

Given that,
Two cylinders are similar. The volume of one is 8cm^3, and the volume of the other is 125cm^3. To determine the scale factor between them.


What is the scale factor?

The scale factor is defined as the ratio of modified change in length to the original length.

Since the volume of any shape is a cubic function, implies
The scale factor of cylinders,
= ∛(volume of one cylinder) / ∛ volume of another cylinder
= ∛8 / ∛125
= 2 / 5

Thus, the required scale factor for the two similar cylinders with the volume of one is 8cm^3, and the volume of the other is 125cm^3 is 2 / 5.

Learn more about line Scale factors here:

https://brainly.com/question/22312172

#SPJ2

Otras preguntas