d
\(\rho=\frac{M}{V}=\frac{M}{\frac{4}{3} \pi\left(\frac{D}{2}\right)^{3}}\)

\(\rho=\frac{6}{\pi} M D ^{-3}\)

taking log

\(\ell n \rho=\ell n \left(\frac{6}{\pi}\right)+\ell n M -3 \ell m D\)

Differentiates

\(\frac{ d p}{\rho}=0+\frac{ d M }{ M }-3 \frac{ d ( D )}{ D }\)

for maximum error

\(100 \times \frac{ d \rho}{\rho}=\frac{ dM }{ M } \times 100+\frac{3 d D }{ D } \times 100\)

\(=6+3 \times 1.5\)

\(=10.5 \%\)

\(=\frac{1050}{100} \%\)

\(x=1050.00\)