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(B) The volume of a cone is given by $V = \frac{1}{3} \pi \left(\frac{D}{2}\right)^2 H = \frac{1}{12} \pi D^2 H$.Taking the relative error,we have $\f

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$3$

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(B) The volume of a cone is given by $V = \frac{1}{3} \pi \left(\frac{D}{2}ight)^2 H = \frac{1}{12} \pi D^2 H$.Taking the relative error,we have $\frac{\Delta V}{V} = 2 \frac{\Delta D}{D} + \frac{\Delta H}{H}$.Given,least count $\Delta D = \Delta H = 2 	ext{ mm} = 0.2 	ext{ cm}$.Measured values $D = H = 20.0 	ext{ cm}$.The percentage error in $D$ is $\frac{\Delta D}{D} 	imes 100\% = \frac{0.2 	ext{ cm}}{20.0 	ext{ cm}} 	imes 100\% = 1\%$.The percentage error in $H$ is $\frac{\Delta H}{H} 	imes 100\% = \frac{0.2 	ext{ cm}}{20.0 	ext{ cm}} 	imes 100\% = 1\%$.Therefore,the maximum percentage error in the volume $V$ is $\frac{\Delta V}{V} 	imes 100\% = 2(1\%) + 1\% = 3\%$.

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

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