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(C) The surface area of a sphere is given by $S = 4\pi r^2$. The relative error in the surface area is $\frac{\Delta S}{S} = 2 \frac{\Delta r}{r} = \a

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$\frac{3}{2}\alpha$

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(C) The surface area of a sphere is given by $S = 4\pi r^2$. The relative error in the surface area is $\frac{\Delta S}{S} = 2 \frac{\Delta r}{r} = \alpha$. From this,the relative error in the radius is $\frac{\Delta r}{r} = \frac{\alpha}{2}$. The volume of a sphere is given by $V = \frac{4}{3}\pi r^3$. The relative error in the volume is $\frac{\Delta V}{V} = 3 \frac{\Delta r}{r}$. Substituting the value of $\frac{\Delta r}{r}$,we get $\frac{\Delta V}{V} = 3 	imes \frac{\alpha}{2} = \frac{3}{2}\alpha$.

The relative error in the determination of the surface area of a sphere is $\alpha$. Then the relative error in the determination of its volume is

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