if the volume of the cube is increased by the factor of 8, what is the change in the length of the sides of the cube?

The new vol = 8 times the old vol.  Therefore the sides of the cube have been made 2 times larger.  (the cube root of 8 is 2.)

Doubled: Volume increased 8 times 
Tripled: Volume increased 27 times 
Quadrupled: Volume increased 64 times 

Pretty simple. If you're doubling the lengths, you're increasing them by 2 times. Take 2 and raise it to the 3rd power. If you're tripling the lengths, you're increasing them 3 times over. Take 3 and raise it to the 3rd power. And so on. 

Doubled = 2^3 = 8 
Tripled = 3^3 = 27 
Quadrupled = 4^3 = 64 

Does that make sense?

this is not the answer this is just a question. is this middle school math?

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