(a) The Volume of the Cube:
V=x3
dxdV=3x2
dV=3x2dx
ΔV=3x2Δx
ΔV=3(30cm)2(0.1cm)=270 cm3 Relative Error:
VΔV=(30 cm)3270 cm3=0.01 Percentage Error:
0.01⋅100%=1%
(b) The Surface Area of the Cube:
A=6x2
dxdA=12x
dA=12xdx
ΔA=12xΔx
ΔA=12(30cm)(0.1cm)=36 cm2 Relative Error:
AΔA=6(30 cm)236 cm2=1501 Percentage Error:
1501⋅100%=32%≈0.67
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