The dimensions of a cone are measured using a scale with a least count of $2 \mathrm{~mm}$. The diameter of…

The dimensions of a cone are measured using a scale with a least count of $2 \mathrm{~mm}$. The diameter of the base and the height are both measured to be $20.0 \mathrm{~cm}$. The maximum percentage error in the determination of the volume is _______ .

Solution

$\mathrm{V}=\frac{1}{3} \pi\left(\frac{\mathrm{D}}{2}\right)^2 \mathrm{H}$ $\therefore \%$ Error in $\mathrm{V}=2$ (% error in $\mathrm{D})+\%$ error in $\mathrm{H}$. $\because$ Least count is $2 \mathrm{~mm}$. $\therefore \%$ error in D $=\frac{2 \mathrm{~mm}}{20 \mathrm{~cm}} \times 100 \%=1 \%$ & % error in $\mathrm{H}=\frac{2 \mathrm{~mm}}{20 \mathrm{~cm}} \times 100 \%=1 \%$ So $\%$ error in $\mathrm{V}=2 \times 1 \%+1 \%=3 \%$

Asked in: JEE Advanced 2024 (Paper 2)

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