The relative error in the determination of th | vedclass

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Question

$\begin{array}{l}
{\mathop{m Re}
olimits} lative\,\,eroor\,\,in\,\,surface\,\,area,\
\frac{{\Delta s}}{s} = 2 	imes \frac{{\Delta r}}{r} = \alp

Vedclass · Accepted Answer

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

Vedclass · Answer

$\begin{array}{l}
{\mathop{m Re}
olimits} lative\,\,eroor\,\,in\,\,surface\,\,area,\
\frac{{\Delta s}}{s} = 2 	imes \frac{{\Delta r}}{r} = \alpha \,and\,relative\,error\,in\
volume,\,\frac{{\Delta v}}{v} = 3 	imes \frac{{\Delta r}}{r}\
	herefore \,{\mathop{m Re}
olimits} lative\,\,error\,in\,volume\,w.r.t\,relative\,error\,in\,area,\
\frac{{\Delta v}}{v} = \frac{3}{2}\alpha 
\end{array}$

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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