Answer with Step-by-step explanation:
We are given that
Side of cube, x=30 cm
Error in measurement of edge,[tex]\delta x=0.5[/tex] cm
(a)
Volume of cube, [tex]V=x^3[/tex]
Using differential
[tex]dV=3x^2dx[/tex]
Substitute the values
[tex]dV=3(30)^2(0.5)[/tex]
[tex]dV=1350 cm^3[/tex]
Hence, the maximum possible error in computing the volume of the cube
=[tex]1350 cm^3[/tex]
Volume of cube, [tex]V=(30)^3=27000 cm^3[/tex]
Relative error=[tex]\frac{dV}{V}=\frac{1350}{2700}[/tex]
Relative error=0.05
Percentage error=[tex]0.05\times 100=5[/tex]%
Hence, relative error in computing the volume of the cube=0.05 and
percentage error in computing the volume of the cube=5%
(b)
Surface area of cube,[tex]A=6x^2[/tex]
[tex]dA=12xdx[/tex]
[tex]dA=12(30)(0.5)[/tex]
[tex]dA=180cm^2[/tex]
The maximum possible error in computing the volume of the cube=[tex]180cm^2[/tex]
[tex]A=6(30)^2=5400cm^2[/tex]
Relative error=[tex]\frac{dA}{A}=\frac{180}{5400}[/tex]
Relative error in computing the volume of the cube=0.033
The percentage error in computing the volume of the cube=[tex]0.033\times 100=3.3[/tex]%
