Question

Find the area ratio of a cube with volume 125 m to a cube with volume 64 m.

Answer 1

V=s^3
SA=6s^2
so

125=v
125=s^3
cube root both sides
5=s
A=6(5)^2=6(25)=150 m^2


64=v
64=s^3
cube root both sides
4=s

A=6(4)^2=6(16)=96 m^2

ratio is

150:96=25:16

Answer 2

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.

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


Now find the area of the sides:

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


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


Thus the answer is 25/16 = 1.5625