Question

The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density of the sphere is $\left(\frac{x}{100}\right)\%.$ If the relative errors in measuring the mass and the diameter are $6.0\%$ and $1.5\%$ respectively, the value of $x$ is

Answer 1

$\rho =\frac{m}{\frac{4}{3} \pi \left(\frac{d}{2}\right)^{3}}$
$\rho =k\cdot \frac{m}{d^{3}}$
$\log\rho =\log k+\log m-3logd$
diff.
$\frac{d \rho }{\rho }=\frac{d m}{m}+3\cdot \frac{d d}{d}$
$=6.0+3\times 1.5=10.5\%$
$=x=1050$