The dimensions of a cone are measured using a scale with a least count of $2 mm$. The diameter of the base and the height are both measured to be $20.0 cm$. The maximum percentage error in the determination of the volume is. . . . .
A$2$
B$3$
C$4$
D$5$
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B$3$
b $V =\frac{1}{3} \pi\left(\frac{ D }{2}\right)^2 H$
$\therefore \%$ Error in $V =2(\%$ error in $D )+\%$ error in $H$.
$\because$ Least count is $2 mm$.
$\therefore \%$ error in D $=\frac{2 mm }{20 cm } \times 100 \%=1 \%$
% error in $H =\frac{2 mm }{20 cm } \times 100 \%=1 \%$
So $\%$ error in $V =2 \times 1 \%+1 \%=3 \%$
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