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So to find the ratio of the *Surface areas you need to find the Area of the sides/faces of the cubes.

*Keep in mind that the faces of a cube are squares.

Surface Area of a cube = Area of a side * 6
Area = length * width
Area of a square = length * length 

We don't know the length/width of the cube, so we need to solve for it using the values for the volumes of the two cubes.

[tex]Volume = length * width* height\\Volume of a cube = length * length * length\\\\125\ m^{3}=length^{3}\\\\\sqrt[3]{125\ m^{3}}=\sqrt[3]{length^{3}}\\\\5\ m=length\\\\\\64\ m^{3}=length^{3}\\\\\sqrt[3]{64\ m^{3}}=\sqrt[3]{length^{3}}\\\\4\ m=length[/tex]


Now find the area of the sides:

[tex] Area = length *length\\\\Area\ of\ cube\ 1=5\ m*5\ m=25\ m^{2}\\\\Surface\ Area\ of\ cube\ 1=side\ area*6\\\\SA_{cube\ 1}=25\ m^{2}*6=150\ m^{2}\\\\\\Area\ of\ cube\ 2=4\ m*4\ m=16\ m^{2}\\\\Surface\ Area\ of\ cube\ 2=side\ area*6\\\\SA_{cube\ 2}=16\ m^{2}*6=96\ m^{2}[/tex]


Now find the ratio between the Surface areas:
[tex]150\ m^{2}:96\ m^{2}\\\\150\6:96\6\\\\25:16=\frac{25}{16}=1\ \frac{9}{16}=1.5625[/tex]


Thus the answer is 25/16 = 1.5625

The required ratio of area of cubes is 25 : 16.

Volume of cube 1 = 125
Volume of cube 2 = 64

What is the Ratio?

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

Volume of cube 1 = 125
    a³ = 125
    a = 5
Volume of cube 2 = 64
       A³ = 64
        A = 4
Area of cube 1 = a² x 6
= 5² x 6
= 150
Area of cube 2 = A² x 6
= 4² x 6
= 96
Now ,
The ratio of areas of cube 1 to cube 2 = 150:96.
= 25:16

Thus, the required ratio of area of cubes is 25 : 16.  

Learn more about ratio here:

brainly.com/question/13419413

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