Question

Please match each drop down answer choice to each selection.

Answer 1

• 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.

`\begin{gathered} \implies(x^3)/(y^3)=(40)/(2) \\ ((x)/(y))^3=20 \end{gathered}`

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.

`(x)/(y)=\sqrt[3]{20}=2.7`

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

Therefore, the ratio of the surface areas will be:

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

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