The radius of a sphere is measured to be (7.5 | vedclass

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(B) The volume of a sphere is given by the formula $V = \frac{4}{3} \pi r^3$.Taking the natural logarithm on both sides,we get $\ln V = \ln(\frac{4}{3

Vedclass · Accepted Answer

$34$

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(B) The volume of a sphere is given by the formula $V = \frac{4}{3} \pi r^3$.Taking the natural logarithm on both sides,we get $\ln V = \ln(\frac{4}{3} \pi) + 3 \ln r$.Differentiating both sides,we obtain the relative error formula: $\frac{\Delta V}{V} = 3 \frac{\Delta r}{r}$.Given $r = 7.50 \, cm$ and $\Delta r = 0.85 \, cm$.The percentage error in volume is given by $\frac{\Delta V}{V} 	imes 100 = 3 	imes (\frac{\Delta r}{r}) 	imes 100$.Substituting the values: $\frac{\Delta V}{V} 	imes 100 = 3 	imes (\frac{0.85}{7.50}) 	imes 100$.$\frac{\Delta V}{V} 	imes 100 = 3 	imes 0.11333 	imes 100 = 34\%$.Thus,the value of $x$ is $34$.

The radius of a sphere is measured to be $(7.50 \pm 0.85) \, cm$. Suppose the percentage error in its volume is $x$. The value of $x$,to the nearest integer is .....$\%$

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