The maximum error in the measurement of mass and density of the cube are 3% and 9% respectively. The maximum error in the measurement of length will be

4%

Density = $\rho$ = $\frac{\text {Mass (M)}}{\text{Volume (V)}} = \frac{M}{V}$

V = $\frac{M}{\rho}$

$\ell^3=\frac{M}{\rho}$

Max. fractional error

$\frac{3 \Delta \ell}{\ell}=\frac{\Delta M}{M}+\frac{\Delta \rho}{\rho}$

Percentage error

$\frac{3 \Delta \rho}{\ell}$% = 3% + 9%

$\frac{\Delta \ell}{\ell} \%=\frac{12}{3}$%

$\frac{\Delta \ell}{\ell}$% = 4%