Answer:
Maximum volume error = ±540 cm³
Relative error = 0.02
Percentage error = 2%
Step-by-step explanation:
Relative error : The ratio of volume error to the total volume.
Percentage error: The product of relative error and 100.
The volume of a cube is = [tex]side^3[/tex]
v =x³
Differentiate with respect to x
[tex]\frac{dv}{dx} = 3x^2[/tex]
[tex]\Rightarrow dv = 3x^2 dx[/tex]
Here are x = 30 cm and dx= ±0.2 cm
∴ dv = 3×(30 cm)² (±0.2 cm)
=±540 cm³
The volume of the cube = 30³ cm ³ = 27,000 cm³
Then the relative error
[tex]=\frac{dv}{v}[/tex]
[tex]=\frac{540 cm^3}{27,000 cm^3}[/tex]
= 0.02.
The percentage error
= (0.02×100)
=2%
