V(r) = (4/3) π r³,V '(r) = 4π r² ,
ΔV ≈ dV = V '(r) dr = V '(r) Δr
1.球中含铁的体积 r = 5,Δr = 5.2 - 5 = 0.2
V铁 ≈ 4π r² Δr = 4 π 5² * 0.2 ≈ 62.832
m铁 ≈ 7.86 * 62.832 ≈ 493.86 (克)
2.球中含金的体积 r = 5.2,Δr = 0.005
V金 ≈ 4π r² Δr = 4 π 5.2² * 0.005 ≈ 1.70
m金 ≈ 18.9 * 1.70 ≈ 32.13 (克)