1) Area of one side of each cube
The area of one side of each cube can be calculated by multiplying the length times the width:
[tex]A=L\cdot W[/tex]
where
L = length
W = width
For cube A: [tex]L=1 cm, W=1 cm[/tex]
So the area is: [tex]A_A = (1)(1)=1 cm^2[/tex]
For cube B: [tex]L=2 cm, W=2 cm[/tex]
So the area is: [tex]A_B=(2)(2)=4 cm^2[/tex]
For cube C: [tex]L=3 cm, W=3 cm[/tex]
So the area is: [tex]A_C=(3)(3)=9 cm^2[/tex]
2) Surface area of each cube
The surface area of a cube is given by the sum of the areas of all its faces. Since a cube has 6 identical faces, this means that the total surface area is equal to 6 times the area of one face:
[tex]A=6 A_1[/tex]
where
[tex]A_1[/tex] is the area of one face of the cube
For cube A, the area of one face is [tex]A_A=1 cm^2[/tex]
So the surface area of cube A is
[tex]A'_A = 6A_A=6(1)=6 cm^2[/tex]
For cube B, the area of one face is [tex]A_B=4 cm^2[/tex]
So the surface area of cube B is
[tex]A'_B = 6A_B=6(4)=24 cm^2[/tex]
For cube C, the area of one face is [tex]A_C=9 cm^2[/tex]
So the surface area of cube C is
[tex]A'_C = 6A_C=6(9)=54 cm^2[/tex]
3) Volume of each cube
The volume of a cube is obtained by multiplying its length, its width and its height:
[tex]V=L\cdot W \cdot H[/tex]
Where:
L = length
W = width
H = height
Moreover for a cube, all the sides have equal length, so [tex]L=W=H[/tex]
So the volume can be rewritten as
[tex]V=L^3[/tex]
For cube A: L = 1 cm
So the volume is [tex]V_A=(1 cm)^3 = 1 cm^3[/tex]
For cube B: L = 2 cm
So the volume is [tex]V_B=(2 cm)^3 = 8 cm^3[/tex]
For cube C: L = 3 cm
So the volume is [tex]V_C = (3 cm)^3 = 27 cm^3[/tex]
4) Ratio surface area/volume for each cube
In this part, we have to calculate the ratio between surface area and volume of each cube:
[tex]r=\frac{A}{V}[/tex]
where
A is the surface area
V is the volume
For cube A, we have:
[tex]A_A = 6 cm ^2[/tex] (surface area)
[tex]V_A=1 cm^3[/tex] (volume)
So the ratio for cube A is:
[tex]r=\frac{6}{1}=6[/tex]
For cube B, we have:
[tex]A_B = 24 cm ^2[/tex] (surface area)
[tex]V_B=8 cm^3[/tex] (volume)
So the ratio for cube B is:
[tex]r=\frac{24}{8}=3[/tex]
For cube C, we have:
[tex]A_C = 54 cm ^2[/tex] (surface area)
[tex]V_C=27 cm^3[/tex] (volume)
So the ratio for cube C is:
[tex]r=\frac{54}{27}=2[/tex]
