Respuesta :
Answer:
Only side length and perimeter of one face
Step-by-step explanation:
Given is a cube with measures given in inches.
For a cube
Volume = s^3 where s = side
Hence volume and side are not having linear relation
Perimeter of 1 face = 4s and area =s^2
Obviously 4s and s^2 cannot have linear relationship as degree is diferent
Surface area of cube = 6s^2 but volume = s^3 both have different degrees of s and hence cannot have linear relation
Area of 1 face = s^2 and surface area = 6s^2
THus we get Surface area = 6(area of 1 face) hence can have linear relationship
side length =s and volume = s^3 so cannot have linear relaionship
Side length =s and perimeter = 4s thus having linear relation.
Hence answers are
side length and perimeter of 1 face
area of 1 face and surface area
A linear relationship is represented by [tex]y = mx + b[/tex], where [tex]m \ne 0[/tex]. The linear relationships are:
- Side length and perimeter of 1 face
- Area of 1 face and surface area
Let
[tex]x \to[/tex] side length of the cube
A. Side length and perimeter of 1 face
The perimeter (P) of one face is:
P = 4 x Side length
[tex]P =4 \times x[/tex]
[tex]P = 4x[/tex]
Compare the above equation to [tex]y = mx + b[/tex].
We can conclude that (a) is a linear relationship
B. Perimeter of 1 face and area of 1 face
We have:
[tex]P = 4x[/tex]
Make x the subject
[tex]x= \frac{P}{4}[/tex]
The area of 1 face is:
[tex]A = x^2[/tex]
Substitute [tex]x= \frac{P}{4}[/tex]
[tex]A = (\frac P4)^2[/tex]
[tex]A = \frac{P^2}{16}[/tex]
Compare the above equation to [tex]y = mx + b[/tex].
We can conclude that (b) is not a linear relationship
C. Surface area and volume
The surface area is:
[tex]S=6x^2[/tex]
The volume is:
[tex]V = x^3[/tex]
Make [tex]x^2[/tex] the subject in [tex]S=6x^2[/tex]
[tex]x^2 = \frac S6[/tex]
So, we have:
[tex]V = x^3[/tex]
[tex]V = \frac S6x[/tex]
Compare the above equation to [tex]y = mx + b[/tex].
We can conclude that (c) is not a linear relationship
D. Area of 1 face and surface area
The surface area is:
[tex]S=6x^2[/tex]
The area of 1 face is:
[tex]A = x^2[/tex]
Substitute [tex]A = x^2[/tex]
[tex]S = 6A[/tex]
Compare the above equation to [tex]y = mx + b[/tex].
We can conclude that (d) is a linear relationship
E. Side length and volume
The volume is:
[tex]V = x^3[/tex]
Compare the above equation to [tex]y = mx + b[/tex].
We can conclude that (e) is a not linear relationship
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