Question

The table below shows the measurements (in inches) from cubes with different side lengths

Answer 1

The answers to your question is,

Side length and perimeter of 1 face AND area of 1 face and surface area.

-Mabel <3

Answer 2

Answer:

1st and 4th Option are correct.

Step-by-step explanation:

Given:

A table with multiple variables.

To find: Linear relationship between variables.

First, between side length and perimeter of 1 face.

Consider, $\frac{side\:length}{Perimeter}=\frac{3}{12}=\frac{1}{4}$

$\frac{4}{16}=\frac{1}{4}$

$\frac{5}{20}=\frac{1}{4}$

$\frac{6}{24}=\frac{1}{4}$

Since all the ratio are equal.

Thus, Both Variables are in Linear Relationship.

Second, between Perimeter of 1 face and Area of 1 face.

$\frac{Perimeter}{Area}=\frac{12}{9}=\frac{4}{3}$

$\frac{16}{16}=1$

Since first two ratio are not equal.

Thus, Both Variables are not in Linear Relationship.

Third, between Surface Area and Volume

$\frac{Surface\:Area}{Volume}=\frac{54}{27}=\frac{2}{1}$

$\frac{96}{64}=\frac{3}{2}$

Since first two ratio are not equal.

Thus, Both Variables are not in Linear Relationship.

Fourth, between Area of 1 face. and Surface Area

$\frac{Area}{Surface\:Area}=\frac{9}{54}=\frac{1}{6}$

$\frac{16}{96}=\frac{1}{6}$

$\frac{25}{150}=\frac{1}{6}$

$\frac{36}{216}=\frac{1}{6}$

Since all the ratio are equal.

Thus, Both Variables are in Linear Relationship.

Fifth, between Side Length and Volume

$\frac{Side\:length}{Volume}=\frac{3}{27}=\frac{1}{9}$

$\frac{4}{64}=\frac{1}{16}$

Since first two ratio are not equal.

Thus, Both Variables are not in Linear Relationship.

Therefore, 1st and 4th Option are correct.