Question

What's the error? Jerry says that a cube with edges that measure 10 cm has a volume that is twice as much as a cube with sides that measure 5 cm. Explain and correct Jerry's error

Answer 1

The quick way to dispute something like this is to simply do the calculation and then create a ratio. 

Cube One (Large Cube)
The formula for a cube is V = e^3 
e = the measurement of an edge. In this case.
e = 10 cm
V = e^3
V = 10^3 = 10*10*10
V = 1000 cm^3

Cube 2 (Small Cube)
V = e^3
e = 5 cm
V = 5*5*5
V = 125 cm^3

Ratio
Large Cube / Small Cube = 1000 / 125 = 8/1.

The difference in size is 8 to 1 not 2 to 1.

Explanation
He's right if he sticks to one side. The ratio of one side of the large cube to the small one is 2 to 1. But once you put that into the formula for volume, three sides are multiplied together and that 2 shows up everytime you multiply the sides together.