Question

the relative error in the determination of the surface area of a sphere is alfa.then the relative error in the determination of volume

Answer 1

S=4πR

2

lnS= ln(4π)+ln(R

2

)

lnS=2lnR

S

ΔS

=2

R

ΔR

=α

R

ΔR

=

2

α

------------(1)

V=

3

4

πR

3

lnV = ln(

3

4

π)+lnR

3

lnV=3lnR

V

ΔV

=3

R

ΔR

V

ΔV

=3(

2

α

)