Question

FIND THE ABSOLUTE ERROR IN DENSITY OF A SPHERE OF RADIUS 10.01cm AND MASS OF SPHERE IS 4.692 kg ?

Answer 1

Find relative error first and multiply by the density to get absolute error.

R = 10.01 cm
V = 4π/3 R³ = 4π/3 * 10.01³ cm³ = 4201.369 cm³
M = 4.692 kg = 4, 692 gms

Density = Mass / volume 
ρ = M / V = (3/4π) M / R³     = 1.1168  gm/cm³

abs. errors:     ΔM = 1 gm           ΔR = 0.01 cm

Relative error in density:
Δρ / ρ  = ΔM / M   +   ΔV / V
           = ΔM / M  +  3 ΔR / R
Δρ / ρ  = 1 / 4692 + 3 * 0.01 /10.01
            = 0.0321

Absolute error in density = 0.0321 * 1.1168 = 0.03584 gm/cm³