Question 8

The volume of a cone is given by $V = \frac{1}{3}\pi r^2 h$. Expressing this in terms of diameter $D$: $V = \frac{1}{3}\pi (\frac{D}{2})^2 h = \frac{\pi D^2 h}{12}$. The maximum fractional error in volume is given by: $\frac{\Delta V}{V} = 2\frac{\Delta D}{D} + \frac{\Delta h}{h}$ Given: Least count $\Delta D = \Delta h = 2\text{ mm} = 0.2\text{ cm}$ Measured values $D = 20.0\text{ cm}$, $h = 20.0\text{ cm}$ Substituting the values: $\frac{\Delta V}{V} = 2\left(\frac{0.2}{20.0}\right) + \frac{0.2}{20.0}$ $\frac{\Delta V}{V} = 3\left(\frac{0.2}{20.0}\right) = 3(0.01) = 0.03$ Percentage error $= \frac{\Delta V}{V} \times 100 = 0.03 \times 100 = 3\%$. Final answer is 3.