The Density Of A Steel Ball Was Determined By Measuring Its Mass And Diameter.

- May 18, 2019-

The mass was measured within 1%, and the diameter within 3%, what is the error in the density of steel ball approximately?


Density of steel ball is given by

d=m/(4/3) (pi)r^3

log(d)=log (m)-log (r^(-3)

Taking log of the two side and differentiating

del (d)/d=del (m)/m+-(-3) del (r)/r

=1+(-3)×3

Maximum possible error in measuring density is (1+3×3)=10% and error lies between

9-1=8% and 10%.