Answer
% error in area is 1%
% error in volume is 1.5%
Work Step by Step
The given % error change in side length: $\frac{dx}{x}$=0.5%
% error change=$\frac{change\ in\ dimension}{original\ dimension} $
$A=6x^2$
$dA=12x dx$
$V=x^3$
$dV=3x^2 dx$
% error in Area=$\frac{dA}{A}=\frac{12x dx}{6x^2}=2\times0.005=0.01$
% error in volume=$\frac{dV}{V}=\frac{3x^2dx}{x^3}=0.015$
