Question

The density of a cube is measured by measuring its mass and the length of its sides. If the maximum errors in the measurement of mass and length are $3\%$ and $2\%$, respectively, then find the maximum error in the measurement of the density of cube.

Answer 1

Maximum error in mass $\frac{\Delta m}{m}\times 100=3$%

% error in length $=2$%

Density $=\frac{Mass}{Volume}$

$\frac{\Delta P}{P}\times 100=[\frac{\Delta m}{m}+\frac{3\Delta l}{l}]\times 100$

$=(3+3\times 2)$%

maximum error in density $=9$%