The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and lengths are 3% and 2% respectively, the maximum error in the measurement of density would be: [PMT/NEET-1996]

a. 12%
b. 14%
c. 7%
d. 9%

Answer: d. 9%

Solution:
For a cube

$$ \rho = \dfrac{m}{l^{3}} $$

Hence

$$ \dfrac{\Delta \rho}{\rho}=\dfrac{\Delta m}{m}+3\dfrac{\Delta l}{l} $$

$$ =3\%+3\times2\%=9\% $$