Question:

The relative error in the determination of the surface area of a sphere is α. Then the relative error in the determination of its volume is :

23α

32α

52α

S=4πR²
lnS=ln(4π)+ln(R²)
lnS=2lnR
ΔS/S=2ΔR/R=α
ΔR/R=α/2 ———(1)
V=4/3πR³
lnV=ln(4/3π)+lnR³
lnV=3lnR
ΔV/V=3ΔR/R
ΔV/V=3(α/2)
ΔV/V=3α/2 = 3/2α