Question

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

Check all that apply

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

1st and 4th Option are correct.

Explanation:

Given:

A table with multiple variables.

To find: Linear relationship between variables.

First, between side length and perimeter of 1 face.

Consider,
`(side\:length)/(Perimeter)=(3)/(12)=(1)/(4)`

`(4)/(16)=(1)/(4)`

`(5)/(20)=(1)/(4)`

`(6)/(24)=(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.

`(Perimeter)/(Area)=(12)/(9)=(4)/(3)`

`(16)/(16)=1`

Since first two ratio are not equal.

Thus, Both Variables are not in Linear Relationship.

Third, between Surface Area and Volume

`(Surface\:Area)/(Volume)=(54)/(27)=(2)/(1)`

`(96)/(64)=(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

`(Area)/(Surface\:Area)=(9)/(54)=(1)/(6)`

`(16)/(96)=(1)/(6)`

`(25)/(150)=(1)/(6)`

`(36)/(216)=(1)/(6)`

Since all the ratio are equal.

Thus, Both Variables are in Linear Relationship.

Fifth, between Side Length and Volume

`(Side\:length)/(Volume)=(3)/(27)=(1)/(9)`

`(4)/(64)=(1)/(16)`

Since first two ratio are not equal.

Thus, Both Variables are not in Linear Relationship.

Therefore, 1st and 4th Option are correct.