Question

If the radius of a sphere is measured as $9cm$ with an error of $0.02cm$, then find the approximate error in calculating its volume.

Answer 1

Volume of a sphere is given by $V=\frac{4\pi R^3}{3}$

$\therefore \frac{\Delta V}{V}=\frac{3\Delta R}{R}$

$\therefore \Delta V=3V\times \frac{\Delta R}{R}$

$=4\pi R^3\times \frac{\Delta R}{R}$

$=4\pi R^2\times \Delta R$

$=4\pi \times 81\times 0.02$

$=20.357c{m}^3$ approximately