If the radius of a sphere is measured as 9 c | vedclass

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(A) Let $r$ be the radius of the sphere and $\Delta r$ be the error in measuring the radius.Given, $r = 9 \ cm$ and $\Delta r = 0.03 \ cm$.The surface

Vedclass · Accepted Answer

$2.16$

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(A) Let $r$ be the radius of the sphere and $\Delta r$ be the error in measuring the radius.Given, $r = 9 \ cm$ and $\Delta r = 0.03 \ cm$.The surface area $S$ of a sphere is given by $S = 4 \pi r^2$.To find the approximate error in the surface area, we differentiate $S$ with respect to $r$:$\frac{dS}{dr} = 8 \pi r$.Using the differential approximation, $\Delta S \approx \frac{dS}{dr} 	imes \Delta r$.Substituting the values:$\Delta S = 8 \pi 	imes 9 	imes 0.03$.$\Delta S = 72 \pi 	imes 0.03 = 2.16 \pi \ cm^2$.Thus, the approximate error in calculating the surface area is $2.16 \pi \ cm^2$.

If the radius of a sphere is measured as $9 \ cm$ with an error of $0.03 \ cm$, then find the approximate error in calculating its surface area. (in $\pi \ cm^2$)

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