The dimensions of a cone are measured using a scale with a least...

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 _______ . The dimensions of a cone are measured using a scale with a least count of 2 ~mm . The diameter of the base and the

The dimensions of a cone are measured using a scale with a least count of 2 ~mm . The diameter of the base and the

Correct answer

Step-by-step 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 \%

\%

error in

\mathrm{V}=2 \times 1 \%+1 \%=3 \%

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