Answer: 8 times.
Step-by-step explanation:
I will answer in English:
This says:
The volume of a cube is 125cm^3
How many times the volume will increase if we duplicate the lenght of the side?
If L is the lenght of the side, we have that the volume of the cube is:
V = L^3
If we duplicate the lenght of the side, the new volume is:
V = (2*L)^3 = 8*L^3
So we can see that the volume of the new cube is 8 times the volume of the previous cube.
Now, we can do the math, for our original cube we have:
L^3 = 125cm^3
L = 5cm
the new cube has L' = 2*L = 10cm
The volume of this cube is:
V' = L'^3 = 10cm^3 = 1000cm^3
the ratio V'/V is:
1000cm^3/125cm^3 = 8
