The density of the material of a cube can be estimated by measuring...

Given, Maximum error in the measurement of mass $=0.3 \%$ Maximum error in the measurement of length $=0.2 \%$ We know that, Error in density is given as, $\text {Density, } \rho=\frac{\text { mass }(m)}{\text { volume }(V)}=\frac{m}{L^{3}}$ where, $L=$ side of cube Error in density is given as, \left(\frac{\Delta \rho}{\rho}\right)=\frac{\Delta m}{m}+\frac{3 \Delta L}{L}$or \left(\frac{\Delta \rho}{\rho}\right) \times 100=\left(\frac{\Delta m}{m}+\frac{3 \Delta L}{L}\right) \times 100$ Substituting the given values, we get \left(\frac{\Delta \rho}{\rho}\right)_{\max }=(0.3 \%+3(0.2) \%=0.3 \%+0.6 \%\therefore$Maximum percentage error measurement of density \left(\frac{\Delta \rho}{\rho}\right)_{\max }=0.9 \%$