The diameter and height of a cylinder are mea | vedclass

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(B) The volume $V$ of a cylinder is given by $V = \pi R^2 h = \frac{\pi}{4} D^2 h$.Given $D = 12.6\, cm$,$\Delta D = 0.1\, cm$,$h = 34.2\, cm$,and $\D

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$4260 \pm 80\, cm^3$

Vedclass · Answer

(B) The volume $V$ of a cylinder is given by $V = \pi R^2 h = \frac{\pi}{4} D^2 h$.Given $D = 12.6\, cm$,$\Delta D = 0.1\, cm$,$h = 34.2\, cm$,and $\Delta h = 0.1\, cm$.First,calculate the volume: $V = \frac{3.14159}{4} 	imes (12.6)^2 	imes 34.2 \approx 4264.4\, cm^3$.Rounding to appropriate significant figures (three significant figures based on the given data),$V = 4260\, cm^3$.Now,calculate the relative error: $\frac{\Delta V}{V} = 2\frac{\Delta D}{D} + \frac{\Delta h}{h}$.$\Delta V = V 	imes (2 	imes \frac{0.1}{12.6} + \frac{0.1}{34.2}) = 4264.4 	imes (0.01587 + 0.00292) \approx 4264.4 	imes 0.01879 \approx 80.13$.Rounding the absolute error to one significant figure,we get $\Delta V = 80\, cm^3$.Thus,the volume is $V = 4260 \pm 80\, cm^3$.

List $I$	List $II$
$(A)$ Young's Modulus $(Y)$	$(I)$ $[M L^{-1} T^{-1}]$
$(B)$ Co-efficient of Viscosity $(\eta)$	$(II)$ $[M L^2 T^{-1}]$
$(C)$ Planck's Constant $(h)$	$(III)$ $[M L^{-1} T^{-2}]$
$(D)$ Work Function $(\phi)$	$(IV)$ $[M L^2 T^{-2}]$

The diameter and height of a cylinder are measured by a meter scale to be $12.6 \pm 0.1\, cm$ and $34.2 \pm 0.1\, cm$,respectively. What will be the value of its volume in appropriate significant figures?

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