Question

If the radius of sphere is measured as $9$cm with an error of $0.03$cm, then find the approximate error in calculating its volume.

Answer 1

$r=9cm$ $\Delta$ $r=0.03cm$

V sphere $=\frac{4}{3}\pi r^3$ $\Delta V=\frac{dv}{dr}\Delta r$

$\Delta V=\frac{4}{3}\pi .3r^2.\Delta r$

$\Delta V=\frac{4}{3}\times \frac{22}{7}\times 3\times 9\times 9\times \frac{0.03}{100}=30.548$ cm