Respuesta :

Answer:

• The scale factor of the volume of the bags is 20.

,

• The scale factor of the dimensions of the two bags is 2.7

,

• The scale factor of the surface areas of the two bags is 7.4

Explanation:

Given:

• The volume of the small bag = 2 pounds.

,

• The volume of the large bag = 40 pounds.

We want to determine the ratio by which the surface area of the small bag increases.

First, given the side lengths of two solids:

• The, ratio of the surface areas, of the two solids is ,the ratio of the square of the side lengths,.

,

• The, ratio of the volume, of the two solids is ,the ratio of the cubes of the side lengths,.

Let the side lengths of the large and small bag be x and y respectively.

[tex]\begin{gathered} \implies\frac{x^3}{y^3}=\frac{40}{2} \\ (\frac{x}{y})^3=20 \end{gathered}[/tex]

The scale factor of the volume of the bags is 20.

Next, find the ratio of the side lengths by taking the cube root of both sides.

[tex]\frac{x}{y}=\sqrt[3]{20}=2.7[/tex]

The scale factor of the dimensions of the two bags is 2.7

Therefore, the ratio of the surface areas will be:

[tex](\frac{x}{y})^2=(\sqrt[3]{20})^2=7.4[/tex]

The scale factor of the surface areas of the two bags is 7.4

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