Question 987649
V = x^3 ... start with the volume of a cube formula


dV/dx = 3x^2 ... apply the derivative with respect to x


dV = 3x^2*dx


dV = 3*11^2*0.01 ... plug in x = 11 and dx = 0.01


dV = 3.63


If the change in x is 0.01 cm, then the approximate change in volume is <font color="red">3.63 cubic cm</font>


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Alternative non-calculus based way to do it


Original Volume:
V = x^3
V = 11^3
V = 1,331


Say the side length is x=11+0.01 = 11.01 now. That makes the volume become
V = 11.01^3
V = 1,334.633301


The difference in the two volumes is 
1,334.633301 - 1,331 = 3.63330099999984 which is approximately 3.63 that we got before


The same applies if you did x = 11-0.01 = 10.99 (the only real difference is that the result of the subtraction would be -3.63, but the absolute value of that leads to the same result)